
Class 
Book. 




SIR JOHN F. W. HERSCHEL, BART. 



OUTLINES OF 
ASTRONOMY 



BY 

SIR JOHN F. W. HERSCHEL 



PART ONE 




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SCIENCE 



SIR JOHN HERSCHEL 

Sir John Frederick William Herschel, Bart., 
the illustrious astronomer, was the only son of Sir F. 
William Herschel. He was born at Slough, Bucking- 
hamshire, England, in the year 1792. His scholastic 
education began at Eton, whence, at the age of seven- 
teen, he was sent to St. John's College, Cambridge, 
where he attained to great eminence in mathematics. 
After leaving the University, he entered upon the study 
of astronomy, and in 1820, assisted by his father, com- 
pleted a mirror of 18 inches diameter and 20 feet focal 
length for a reflecting telescope. This, as subsequently 
improved, became the instrument which enabled him to 
effect the astronomical observations that formed the basis 
of his fame. In 1821-23 he undertook the re-examina- 
tion of his father's double stars. For this work he re- 
ceived in 1826 the gold medal of the Astronomical So- 
ciety, and the Lalande Medal of the French Institute. 
From 1824 to 1827 he was Secretary of the Eoyal So- 
ciety, and in 1827 was elected to the Chair of the As- 
tronomical Society, which office he filled on two subse- 
quent occasions. In 1831 the honor of knighthood was 
conferred on him by William IV"., and he subsequently 

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4 SIR JOHN HERSCHEL 

was made a baronet. His exploration of the southern 
heavens constituted an epoch in astronomy, and secured 
for him the distinction of memberships in almost every 
importaat society in both hemispheres. His "Outlines 
of Astronomy," here reproduced, first appeared in 1849, 
and, notwithstanding the disadvantage arising from the 
practice of stereotyping text- books which relate to pro- 
gressive sciences, there is no more instructive volume 
extant on the subject of which it treats. Sir John Her- 
schel died in 1871; his remains are interred in West- 
minster Abbey, close to the grave of Sir Isaac Newton. 



CONTENTS 



Preface to the First Edition ...,..*. 11 

Preface to the Fifth Edition 15 

Preface to the Tenth Edition . . . . , . , . 18 

Introduction .......... , . 21 

PART I 

CHAPTER I 

General Notions — Apparent and real Motions — Shape and Size of the Earth 
— The Horizon and its Dip — The Atmosphere — Refraction — Twilight — 
Appearances resulting from Diurnal Motion — From Change of Station 
in General — Parallactic Motions — Terrestrial Parallax — That of the 
Stars Insensible — First Step toward forming an Idea of the Distance 
of the Stars — Copernican View of the Earth's Motion — Relative Mo- 
tion — Motions partly Real, partly Apparent — Geocentric Astronomy, 
or Ideal Reference of Phenomena to the Earth's Centre as a Common 
Conventional Station 32 

CHAPTER n 

Terminology and Elementary Geometrical Conceptions and Relations — Ter- 
minology relating to the Globe of the Earth — To the Celestial Sphere 
— Celestial Perspective 89 

CHAPTER HI 

Of the Nature of Astronomical Instruments and Observations in General 
— Of Sidereal and Solar Time— Of the Measurements of Time— 
Clocks, Chronometers — Of Astronomical Measurements — Principle of 
Telescopic Sights to Increase the Accuracy of Pointing — Simplest 
Application of this Principle — The Transit Instrument — Of the Meas- 
urement of Angular Intervals — Methods of Increasing the Accuracy of 
Reading — The Vernier — The Microscope — Of the Mural Circle — The 

(5) 



6 CONTENTS 

Meridian Circle — Fixation of Polar and Horizontal Points — The Level, 
Plumb-line, Artificial Horizon — Principle of Collimation — Collimators 
of Rittenhouse, Kater and Bohnenberger — Of Compound Instruments 
with Co-ordinate Circles — The Equatorial, Altitude and Azimuth In- 
strument — Theodolite — Of the Sextant and Reflecting Circle — Principle 
of Repetition — Of Micrometers — Parallel "Wire Micrometer — Principle 
of the Duplication of Images — The Heliometer — Double Refracting 
Bye-piece — Yariable Prism Micrometer — Of the Position Micrometer 
— Illumination of "Wires — Solar Telescope and Eye -piece — Helioscopy 
— Collimation of large Reflectors « lOi 

CHAPTER IV 

OP GEOGRAPHY 

Of the Figure of the Earth — Its Exact Dimensions — Its Form that of Equi- 
librium Modified by Centrifugal Force — Variation of Gravity on its 
Surface — Statical and Dynamical Measures of Gravity — The Pendulum 
— Gravity to a Spheroid — Other Effects of the Earth's Rotation — Trade 
"Winds — Veering of the "Winds — Cyclones — Foucault's Pendulum — The 
Gyroscope — Determination of Geographical Positions — Of Latitudes — 
Of Longitudes — Conduct of a Trigonometrical Survey — Of Maps — Pro- 
jections of the Sphere — Measurement of Heights by the Barometer . It3 

CHAPTER V 

OP URANOGRAPHY 

Construction of Celestial Maps and Globes by Observations of Right Ascen- 
sion and Declination — Celestial Objects Distinguished into Fixed and 
Erratic — Of the Constellations — Natural Regions in the Heavens — The 
Milky "Way — The Zodiac — Of the Ecliptic — Celestial Latitudes and 
Longitudes — Precession of the Equinoxes— Nutation — Aberration — 
Refraction — Parallax — Summary View of the Uranographical Cor- 
rections 246 

CHAPTER VI 

OP THE SUN'S MOTION AND PHYSICAL CONSTITUTION 

Apparent Motion of the Sun not Uniform — Its Apparent Diameter also 
Variable — Variation of its Distance Concluded — Its Apparent Orbit 
an Ellipse about the Focus— Law of the Angular Velocity— Equable 
Description of Areas — Parallax of the Sun — Its Distance and Magni- 
tude — Copernican Explanation of the Sun's Apparent Motion — Parallel- 
ism of the Earth's Axis — The Seasons — Heat Received from the Sud 



CONTENTS 7 

in Different Parts of the Orbit — Effect of Excentricity of the Orbit and 
Position of its Axis on Climate — Mean and True Longitudes of the Sun 
— Equation of the Centre — Sidereal, Tropical and Anomalistic Years 
— Physical Constitution of the Sun — Its Spots — Faculae — Probable 
Nature and Cause of the Spots — Recent Discoveries of Mr. Dawes — 
Of Mr. Nasmyth — Potation of the Sun on its Axis — Its Atmosphere 
. — Supposed Clouds — Periodical Recurrence of a More and Less Spotted 
State of its Surface — Temperature of its Surface — Its Expenditure of 
Heat — Probable Cause of Solar Radiation 281 

CHAPTER YII 

Of the Moon — Its Sidereal Period — Its Apparent Diameter — Its Parallax 
Distance, and Real Diameter — First Approximation to its Orbit — An 
Ellipse about the Earth in the Focus — Its Excentricity and Inclina- 
tion — Motion of its Nodes and Apsides — Of Occupations and Solar 
Eclipses Generally — Limits within which they are Possible — They 
Prove the Moon to be an Opaque Solid — Its Light Derived from the 
Sun — Its Phases — Synodic Revolution or Lunar Monlh — Harvest 
Moon — Of Eclipses more Particularly — Their Phenomena — Their Pe- 
riodical Recurrence — Physical Constitution of the Moon — Its Moun- 
tains and other Superficial Features — Indications of former Volcanic 
Activity — Its Atmosphere — Climate — Radiation of Heat from its Sur- 
face — Rotation on its own Axis — Libration — Appearance of the Earth 
from it — Probable Elongation of the Moon's Figure in the Direction of 
the Earth — Its Habitability not Impossible — Charts, Models and Pho- 
tographs of its Surface ......... 333 

CHAPTER Till 

Of Terrestrial Gravity — Of the Law of Universal Gravitation — Paths of Pro- 
jectiles ; Apparent, Real — The Moon Retained in her Orbit by Gravity 
— Its Law of Diminution — Laws of Elliptic Motion — Orbit of the Earth 
Round the Sun in Accordance with these Laws — Masses of the Earth 
and Sun Compared — Density of the Sun — Force of Gravity at its Sur- 
face — Disturbing Effect of the Sun on the Moon's Motion . . . 336 

CHAPTER IX 

OF THE SOLAR SYSTEM 

Apparent Motions of the Planets— Their Stations and Retrogradations— The 
Sun their Natural Centre of Motion — Inferior Planets — Their Phases, 
Periods, etc. — Dimensions and Form of their Orbits — Transits across 
the Sun — Superior Planets — Their Distances, Periods, etc. — Kepler's 



O CONTENTS 

Laws and their Interpretation — Elliptic Elements of a Planet's Orbit 
— Its Heliocentric and Geocentric Place — Empirical Law of Planetary 
Distances ; Violated in the Case of Neptune — The Asteroids — Physical 
Peculiarities Observable in each of the Planets 319 

CHAPTER X 

OP THE SATELLITES 

Of the Moon, as a Satellite of the Earth — General Proximity of Satellites 
to their Primaries, and Consequent Subordination of their Motions — 
Masses of the Primaries Concluded from the Periods of their Satellites 
— Maintenance of Kepler's Laws in the Secondary Systems — Of Jupi- 
ter's Satellites — Their Eclipses, etc. — Telocity of Light Discovered 
by their Means — Satellites of Saturn — Of Uranus — Of Neptune . 444 



TO 

THE REV. W. RUTTER DAWES, F.R.A.S., 

&c. &c. &c. 

My dear Mr. Dawes — In availing myself of your 
permission to dedicate to you an Edition of these Out- 
lines, enriched by accounts of several of your own re- 
cent discoveries, 1 should ill acquit myself to my own 
feelings if I did not add to the expression of that 
grateful sense of your many and important services to 
our common Science, which every astronomer must ac- 
knowledge, that of affectionate esteem and regard, the 
natural result of a prolonged and most friendly inter- 
course. 

Believe me, 

Yery truly yours, 

J. F. W. Herschel. 

Collingwood, Feb. 15, 1858. 



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PREFACE TO THE FIRST EDITION 

The work here offered to the Public is based "upon and 
may be considered as an extension, and, it is hoped, an 
improvement of a treatise on the same subject, forming 
Part 43 of the Cabinet Cyclopaedia, published in the year 
1833. Its object and general character are sufficiently stated 
in the introductory chapter of that volume, here reprinted 
with little alteration; but an opportunity having been 
afforded me by the Proprietors, preparatory to its reap- 
pearance in a form of more pretension, I have gladly 
availed myself of it, not only to correct some errors 
which, to my regret, subsisted in the former volume, but 
to remodel it altogether (though in complete accordance 
with its original design as a work of explanation); to intro- 
duce much new matter in the earlier portions of it; to re- 
write, upon a far more matured and comprehensive plan, 
the part relating to the lunar and planetary perturbations, 
and to bring the subjects of sidereal and nebular astronomy 
to the level of the present state of our knowledge in those 
departments. 

The chief novelty in the volume, as it now stands, will 
be found in the manner in which the subject of Perturba- 
tions is treated. It is not — it cannot be made elementary, in 
the sense in which that word is understood in these days 
of light reading. The chapters devoted to it must, there- 
fore, be considered as addressed to a class of readers in pos- 
session of somewhat more mathematical knowledge than 

(ii) 



12 PREFACE TO THE FIRST EDITION 

those who will find the rest of the work readily and easily 
accessible; to readers desirous of preparing themselves, by 
the possession of a sort of carte du pays, for a campaign in 
the most difficult, but at the same time the most attractive 
and the most remunerative of all the applications of modern 
geometry. More especially they may be considered as ad- 
dressed to students in that university, where the "Prin- 
cipia" of Newton is not, nor ever will be, put aside as an 
obsolete book, behind the age ; and where the grand though 
rude outlines of the lunar theory, as delivered in the 
eleventh section of that immortal work, are studied less 
for the sake of the theory itself, than for the spirit of far- 
reaching thought, superior to and disencumbered of tech- 
nical aids, which distinguishes that beyond any other pro- 
duction of the human intellect. 

In delivering a rational as distinguished from a technical 
exposition of this subject, however, the course pursued by 
Newton in the section of the "Principia" alluded to, has 
by no means been servilely followed. As regards the per- 
turbations of the nodes and inclinations, indeed, nothing 
equally luminous can ever be substituted for his explana- 
tion. But as respects the other disturbances, the point of 
view chosen by Newton has been abandoned for another, 
which it is somewhat difficult to perceive why he did not, 
himself, select. By a different resolution of the disturbing 
forces from that adopted by him, and by the aid of a few 
obvious conclusions from the laws of elliptic motion which 
would have found their place, naturally and consecutively, 
as corollaries of the seventeenth proposition of his first book 
(a proposition which seems almost to have been prepared 
with a special view to this application), the momentary 
change of place of the upper focus of the disturbed ellipse 



PREFACE TO THE FIRST EDITION 13 

is brought distinctly under inspection: and a clearness of 
conception introduced into the perturbations of the excen- 
tricities, perihelia, and epochs which the author does not 
think it presumption to believe can be obtained by no other 
method, and which certainly is not obtained by that from 
which it is a departure. It would be out of keeping with 
the rest of the work to have introduced into this part of it 
any algebraic investigations; else it would have been easy 
to show that the mode of procedure here followed leads 
direct, and by steps (for the subject) of the most elemen- 
tary character, to the general formulae for these perturba- 
tions, delivered by Laplace in the Mecanique Celeste. 1 

The reader will find one class of the lunar and planetary 
inequalities handled in a very different manner from that 
in which their explanation is usually presented. It com- 
prehends those which are characterized as incident on the 
epoch, the principal among them being the annual and 
secular equations of the moon, and that very delicate and 
obscure part of the perturbational theory (so little satisfac- 
tory in the manner in which it emerges from the analytical 
treatment of the subject), the constant or permanent effect 
of the disturbing force in altering the disturbed orbit. I 
will venture to hope that what is here stated will tend to 
remove some rather generally diffused misapprehensions as 
to the true bearings of Newton's explanation of the annual 
equation. 2 

If proof were wanted of the inexhaustible fertility of 
astronomical science in points of novelty and interest, it 
would suffice to adduce the addition to the list of members 



1 Livre ii. chap. viii. art. 67. 

2 Principia, lib. i. prop. 66, cor. 6. 



14 PREFACE TO THE FIRST EDITION 

of our system of no less than eight new planets and satel- 
lites during the preparation of these sheets for the press. 
Among them is one whose discovery must ever be regarded 
as one of the noblest triumphs of theory. In the account 
here given of this discovery, I trust to have expressed my- 
self with complete impartiality; and in the exposition of 
the perturbative action on Uranus, by which the existence 
and situation of the disturbing planet became revealed to 
us, I have endeavored, in pursuance of the general plan of 
this work, rather to exhibit a rational view of the dynamical 
action, than to convey the slightest idea of the conduct of 
those masterpieces of analytical skill which the researches 
of Messrs. Leverrier and Adams exhibit. 

To the latter of these eminent geometers, as well as to 
my excellent and esteemed friend the Astronomer Koyal, 
I have to return my best thanks for communications which 
would have effectually relieved some doubts I at one period 
entertained had I not succeeded in the interim in getting 
clear of them as to the compatibility of my views on the sub- 
ject of the annual equation already alluded to with the 
tenor of Newton's account of it. To my valued friend, 
Professor De Morgan, I am indebted for some most ingen- 
ious suggestions on the subject of the mistakes committed 
in the early working of the Julian reformation of the calen- 
dar, of which I should have availed myself, had it not ap- 
peared preferable, on mature consideration, to present the 
subject in its simplest form, avoiding altogether entering 
into minutiae of chronological discussion. 

J. F. W. Herschel. 

Collingwood, April 12, 1849. 



PREFACE TO THE FIFTH EDITION 

The rapid progress of science renders it necessary fre- 
quently to revise and bring up elementary works to the 
existing state of knowledge, under penalty of their becom- 
ing obsolete. In former editions of this work, this has been 
done, so far as it could be done without incurring the neces- 
sity of an almost total typographical reconstruction. But 
Astronomy, within the last few years, has been enriched by 
so many and such considerable additions, that it has been 
considered preferable (another edition being called for), not 
indeed to recast the general plan of the work, but to incor- 
porate these in it in due order and sequence, thereby mate- 
rially enlarging the volume, and giving it in many respects 
the air of a new work. The articles thus introduced are 
distinguished from those of the former editions between 
which they have been inserted by the addition to the last 
current number of an italic letter — thus, between Arts. 394 
and 395 will be found inserted 394 a, 394 b, and 394 c. The 
inclosure of any passage in brackets [ ] indicates its having 
been introduced in the Fourth or some subsequent Edition. 
The index references in this as in former editions, being to 
the articles and not to the pages, are thus preserved. To- 
gether with these recent accessions to our knowledge, I 
have taken the opportunity of introducing several things 
which might justly have been noted as deficient in the 
former editions — as, for instance, the account of the meth- 
ods by which the mass of the Earth has been determined, 

(15) 



16 PREFACE TO THE FIFTH EDITION 

and that of the successful treatment, and it is presumed 
final subjugation, of those rebellious ancient Solar Eclipses 
which have so much harassed astronomers. A brief ac- 
count of M. Foucault's remarkable pendulum experiments, 
and of that beautiful instrument, the gyroscope, is intro- 
duced: as are also notices of Professor Thomson's specula- 
tions on the origin of the Sun's heat, and his estimate of 
its average expenditure, as well as of some curious views of 
M. Jean Keynaud, on the secular variation of our climates, 
supplementary to those put forward in former editions of 
this work. I could have wished that its nature and limits 
would have permitted some account of Mr. Cooper's mag- 
nificent contributions to sidereal astronomy, in his cata- 
logue of upward of 60,000 previously unregistered ecliptic 
stars; of Mr. Bishop's ecliptic charts and those of M. Cha- 
cornac; of Mr. Carrington's elaborate circumpolar cata- 
logue; and of Mr. Jones's immense work on the zodiacal 
light, forming the third volume of the account of the United 
States' Japan Expedition, which reached me too late to 
allow of drawing up a fitting analysis of his results. These 
gentlemen will severally please to accept, however, this 
respectful tribute of my admiration for their important 
labors. Some new speculations are also hazarded; as, for 
instance, on the subject of the Moon's habitability, the 
cause of the acceleration of Encke's comet, etc., and a few 
numerical errors are corrected which have hitherto escaped 
notice and public comment as blemishes — as, for example, 
in some of the numbers in Art. 422 in the explanation of 
the phenomena of a lunar eclipse, in the evaluation of the 
total mass of the atmosphere, Art. 242, and in the distance 
of the Moon, Art. 403 (for which, however, I am not 
answerable). 



PREFACE TO THE FIFTH EDITION 17 

In the numerical statement of special astronomical ele- 
ments, it is unavoidable that slightly different values of the 
same quantity should from time to time come to be substi- 
tuted for those before received, as its determination acquires 
additional exactness. To have altered the figures in such 
cases wherever they occur, throughout the letter-press, 
would have entailed, a great probability of error and con- 
fusion; and, as the Synoptic Tables of astronomical ele- 
ments at the end of the work have been carefully revised 
in conformity with the best current authorities, the reader 
is requested, whenever he may observe any discrepancy of 
this nature, to prefer the tabulated values. 

Several of the woodcuts, which were originally drawn 
correctly, have been inverted right hand for left by the 
engraver. So far as explanation goes, this is not of the 
slightest moment. To a reader in the Southern Hemi- 
sphere, they are right as they stand; and one in the 
Northern has only to imagine himself so situated. 

John F. W. Herschel. 

Collingwood, February 17, 1858. 



Note (added in 1865). The views of M. Reynaud, above referred to, though 
no doubt original on his part, are, however, completely anticipated by certain 
speculations of Sir Charles Lyell, in his "Principles of Geology" (p. 110, Ed. of 
1830), expanded and further reasoned out to conclusions identical with those 
of M. Reynaud, in a paper by the author of the present work, "On the Astro- 
nomical Causes which may influence Geological Phenomena, ' ' read before the 
Geological Society on December 15, 1830, and published in the Transactions of 
that Society. This, however, had completely escaped his recollection when 
perusing the works of M. Reynaud referred to in the note to Art. 369 c, which 
occurring while the additions to the Fifth Edition were in preparation, with all 
the force of novelty, led to their insertion in Art. 369 b, and to the above 
notice of them in the preface. 



PREFACE TO THE TENTH EDITION 

Since the publication of the last edition of this work, 
the progress of astronomical discovery has been continuous 
and rapid ; to keep up with which, so far as consistent with 
its general object, it has been necessary to extend some of 
the Notes added in former editions and to annex others. 
Among these recent additions to astronomical knowledge 
may be mentioned more especially those which relate to 
the physical constitution of the central body of our own 
system, on which so vast and unexpected an amount of 
information has accumulated from various quarters as to 
place us at the opening out of a new vista of solar discovery. 
Within the limits of our own system, too, the meteorites 
have at length acquired a firm footing as a distinct group 
of members, while their now established and most unex- 
pected connection with periodic comets in some instances, 
presents the latter class of bodies under a new aspect, in- 
creasing, if anything can increase, the mysterious interest 
which already hangs about them. The group of asteroids, 
too, has received an accession of no less than fifteen to their 
list as it stood at the end of 1866. The elements of these 
are given in the Appendix (from the Berlin "Ephemeris" 
for 1871), so as to complete the list up to the present time. 
The correction indicated in a former edition, as required in 
the distance of the sun (and by necessary implication in the 
dimensions of all the planetary orbits and the magnitudes 
of the sun and planets themselves), has moreover received 
(18) 



PREFACE TO THE TENTH EDITION 19 

an unexpected confirmation from Mr. Stone's critical re- 
examination of the calculations of that distance from the 
recorded observations of the celebrated transit of Venus in 
1769, the result of which is here brought under the notice 
of our readers. 

Beyond the limits of our own system, the application 
of spectrum analysis has disclosed the amazing fact of the 
gaseous constitution of many of the nebulae (a constitution 
long suspected on general cosmological grounds): by which 
is meant their analogy to matter not in that state of lumi- 
nosity presented by the photosphere of our sun, but in that 
in which are maintained the luminous prominences and ap- 
pendages which fringe its disk in total eclipses, a state to 
which the epithet of incandescent- gaseous as distinct from 
flame or a state of combustion seems most appropriate. 
Thus a real line of demarcation between nebulae proper 
and sidereal clusters is decisively drawn. These delicate 
applications of optical science to chemistry have also 
afforded strong grounds for concluding with considerable 
confidence the presence of several of our terrestrial ele- 
mentary bodies in the sun and fixed stars: while in one 
instance prismatic observation has afforded, with a certain 
approach to probability, evidence of the recess of the most 
conspicuous among them from our system, and even sup- 
plied a measure of its rapidity. 

J. F. W. Herschel. 

Collingwood, July 17, 1869. 



OUTLINES OF ASTRONOMY 



INTRODUCTION 

(1.) Every student who enters upon a scientific pursuit, 
especially if at a somewhat advanced period of life, will 
find not only that he has much to learn, but much also to 
unlearn. Familiar objects and events are far from present- 
ing themselves to our senses in that aspect and with those 
connections under which science requires them to be viewed, 
and which constitute their rational explanation. There is, 
therefore, every reason to expect that those objects and 
relations which, taken together, constitute the subject he 
is about to enter upon will have been previously appre- 
hended by him, at least imperfectly, because much has 
hitherto escaped his notice which is essential to its right 
understanding: and not only so, but too often also errone- 
ously, owing to mistaken analogies, and the general prev- 
alence of vulgar errors. As a first preparation, therefore, 
for the course he is about to commence, he must loosen his 
hold on all crude and hastily adopted notions, and must 
strengthen himself, by something of an effort and a resolve, 
for the unprejudiced admission of any conclusion which 
shall appear to be supported by careful observation and 
logical argument, even should it prove of a nature adverse 
to notions he may have previously formed for himself, or 
taken up, without examination, on the credit of others. 

(21) 



22 OUTLINES OF ASTRONOMY 

Such an effort is, in fact, a commencement of that intel- 
lectual discipline which forms one of the most important 
ends of all science. It is the first movement of approach 
toward that state of mental purity which alone can fit us 
for a full and steady perception of moral beauty as well 
as physical adaptation. It is the "euphrasy and rue" with 
which we must "purge our sight" before we can receive 
and contemplate as they are the lineaments of truth and 
nature. 

(2.) There is no science which, more than astronomy, 
stands in need of such a preparation, or draws more largely 
on that intellectual liberality which is ready to adopt what- 
ever is demonstrated, or concede whatever is rendered 
highly probable, however new and uncommon the points 
of view may be in which objects the most familiar may 
thereby become placed. Almost all its conclusions stand 
in open and striking contradiction with those of superficial 
and vulgar observation, and with what appears to every one, 
until he has understood and weighed the proofs to the con- 
trary, the most positive evidence of his senses. Thus, the 
earth on which he stands, and which has served for ages as 
the unshaken foundation of the firmest structures, either of 
art or nature, is divested by the astronomer of its attribute 
of fixity, and conceived by him as turning swiftly on its 
centre, and at the same time moving onward through space 
with great rapidity. The sun and the moon, which appear 
to untaught eyes round bodies of no very considerable size, 
become enlarged in his imagination into vast globes — the 
one approaching in magnitude to the earth itself, the other 
immensely surpassing it. The planets, which appear only 
as stars somewhat brighter than the rest, are to him spa- 
cious, elaborate, and habitable worlds; several of them 



INTRODUCTION 23 

much greater and far more curiously furnished than the 
earth he inhabits, as there are also others less so; and 
the stars themselves, properly so called, which to ordinary 
apprehension present only lucid sparks or brilliant atoms, 
are to him suns of various and transcendent glory— efful- 
gent centres of life and light to myriads of unseen worlds. 
So that when, after dilating his thoughts to comprehend 
the grandeur of those ideas his calculations have called up, 
and exhausting his imagination and the powers of his lan- 
guage to devise similes and metaphors illustrative of the 
immensity of the scale on which his universe is con- 
structed, he shrinks back to his native sphere, he finds 
it, in comparison, a mere point; so lost — even in the 
minute system to which it belongs — as to be invisible 
and unsuspected from some of its principal and remoter 
members. 

(3.) There is hardly anything which sets in a stronger 
light the inherent power of truth over the mind of man, 
when opposed by no motives of interest or passion, than 
the perfect readiness with which all these conclusions are 
assented to as soon as their evidence is clearly apprehended, 
and the tenacious hold they acquire over our belief when 
once admitted. In the conduct, therefore, of this volume, 
I shall take it for granted that the reader is more desirous 
to learn the system which it is its object to teach, as it now 
stands, than to raise or revive objections against it; and 
that, in short, he comes to the task with a willing mind; 
an assumption which will not only save the trouble of 
piling argument on argument to convince the sceptical, but 
will greatly facilitate his actual progress; inasmuch as he 
will find it at once easier and more satisfactory to pursue 
from the outset a straight and definite path, than to be con- 



24 OUTLINES OF ASTRONOMY 

stantly stepping aside, involving himself in perplexities and 
circuits, which, after all, can only terminate in finding him- 
self compelled to adopt the same road. 

(4.) The method, therefore, we propose to follow in this 
work is neither strictly the analytic nor the synthetic, but 
rather such a combination of both, with a leaning to the 
latter, as may best suit with a didactic composition. Its 
object is not to convince or refute opponents, nor to in- 
quire, under the semblance of an assumed ignorance, for 
principles of which we are all the time in full possession — 
but simply to teach what is known. The moderate limit 
of a single volume, to which it will be confined, and the 
necessity of being on every point, within that limit, rather 
diffuse and copious in explanation, as well as the eminently 
matured and ascertained character of the science itself, 
render this course both practicable and eligible. Practi- 
cable, because there is now no danger of any revolution in 
astronomy, like those which are daily changing the features 
of the less advanced sciences, supervening, to destroy all 
our hypotheses, and throw our statements into confusion. 
Eligible, because the space to be bestowed, either in com- 
bating refuted systems, or in leading the reader forward by 
slow and measured steps from the known to the unknown, 
may be more advantageously devoted to such explanatory 
illustrations as will impress on him a familiar and, as it 
were, a practical sense of the sequence of phenomena, and 
the manner in which they are produced. We shall not, 
then, reject the analytic course where it leads more easily 
and directly to our objects, or in any way fetter ourselves 
by a rigid adherence to method. Writing only to be under- 
stood, and to communicate as much information in as little 
space as possible, consistently with its distinct and effectual 



INTRODUCTION 25 

communication, no sacrifice can be afforded to system, to 
form, or to affectation. 

(5.) We shall take for granted, from the outset, the 
Copernican system of the world; relying on the easy, 
obvious, and natural explanation it affords of all the phe- 
nomena as they come to be described, to impress the student 
with a sense of its truth, without either the formality of 
demonstration or the superfluous tedium of eulogy, calling 
to mind that important remark of Bacon — "Theoriarum 
vires, arcta et quasi se mutuo sustinente partium adapta- 
tione, qua quasi in orbem cohasrent, firmantur' ' ; ' not fail- 
ing, however, to point out to the reader, as occasion offers, 
the contrast which its superior simplicity offers to the com- 
plication of other hypotheses. 

(60) The preliminary knowledge which it is desirable 
that the student should possess, in order for the more ad- 
vantageous perusal of the following pages, consists in the 
familiar practice of decimal and sexagesimal arithmetic, 
some moderate acquaintance with geometry and trigonome- 
try, both plane and spherical; the elementary principles of 
mechanics; and enough of optics to understand the con- 
struction and use of the telescope, and some other of the 
simpler instruments. Of course, the more of such knowl- 
edge he brings to the perusal, the easier will be his prog- 
ress, and the more complete the information gained; but 
we shall endeavor in every case, as far as it can be done 
without a sacrifice of clearness, and of that useful brevity 
which consists in the absence of prolixity and episode, 



1 "The confirmation of theories relies on the compact adaptation of their 
parts, by which, like those of an arch or dome, they mutually sustain each 
other, and form a coherent whole. " This is what Dr. Whewell expressively 
terms the consilience of inductions. 
Astronomy — Vol. XIX. — 2 



26 OUTLINES OF ASTRONOMY 

to render what we have to say as independent of other 
books as possible. 

(7.) After all, I must distinctly caution such of my read- 
ers as may commence and terminate their astronomical 
studies with the present work (though of such — at least in 
the latter predicament — I trust the number will be few), 
that its utmost pretension is to place them on the threshold 
of this particular wing of the temple of Science, or rather 
on an eminence exterior to it, whence they may obtain 
something like a general notion of its structure; or, at 
most, to give those who may wish to enter a ground-plan 
of its accesses, and put them in possession of the password. 
Admission to its sanctuary, and to the privileges and feel- 
ings of a votary, is only to be gained by one means — sound 
and sufficient knowledge of mathematics, the great instrument 
of all exact inquiry, without which no man can ever make 
such advances in this or any other of the higher departments 
of science as can entitle him to form an independent opinion 
on any subject of discussion within their range. It is not 
without an effort that those who possess this knowledge can 
communicate on such subjects with those who do not, and 
adapt their language and their illustrations to the necessi- 
ties of such an intercourse. Propositions which to the one 
are almost identical, are theorems of import and difficulty 
to the other; nor is their evidence presented in the same 
way to the mind of each. In teaching such propositions, 
under such circumstances, the appeal has to be made, not 
to the pure and abstract reason, but to the sense of analogy 
— to practice and experience: principles and modes of action 
have to be established not by direct argument from ac- 
knowledged axioms, but by continually recurring to the 
sources from which the axioms themselves have been 



INTRODUCTION 27 

drawn: viz., examples; that is to say, by bringing forward 
and dwelling on simple and familiar instances in which the 
same principles and the same or similar modes of action 
take place: thus erecting, as it were, in each particular 
case, a separate induction, and constructing at each step a 
little body of science to meet its exigencies. The difference 
is that of pioneering a road through an untraversed country 
and advancing at ease along a broad and beaten highway; 
that is to say, if we are determined to make ourselves dis- 
tinctly understood, and will appeal to reason at all. As for 
the method of assertion, or a direct demand on the faith of 
the student (though in some complex cases indispensable, 
where illustrative explanation would defeat its own end by 
becoming tedious and burdensome to both parties), it is one 
which I shall neither willingly adopt nor would recommend 
to others. 

(8.) On the other hand, although it is something new to 
abandon the road of mathematical demonstration in the 
treatment of subjects susceptible of it, and to teach any 
considerable branch of science entirely or chiefly by the 
way of illustration and familiar parallels, it is yet not im- 
possible that those who are already well acquainted with 
our subject, and whose knowledge has been acquired by 
that confessedly higher practice which is incompatible with 
the avowed objects of the present work, may yet find their 
account in its perusal — for this reason, that it is always of 
advantage to present any given body of knowledge to the 
mind in as great a variety of different lights as possible. It 
is a property of illustrations of this kind to strike no two 
minds in the same manner, or with the same force ; because 
no two minds are stored with the same images, or have ac- 
quired their notions of them by similar habits. Accord- 



28 OUTLINES OF ASTRONOMY 

ingly, it may very well happen, that a proposition, even to 
one best acquainted with it, may be placed not merely in a 
new and uncommon, but in a more impressive and satisfac- 
tory light by such a course — some obscurity may be dissi- 
pated, some inward misgivings cleared up, or even some 
links supplied which may lead to the perception of connec- 
tions and deductions altogether unknown before. And the 
probability of this is increased when, as in the present 
instance, the illustrations chosen have not been studiously 
selected from books, but are such as have presented them- 
selves freely to the author's mind as being most in harmony 
with his own views; by which, of course, he means to lay 
no claim to originality in all or any of them beyond what 
they may really possess. 

(9.) Besides, there are cases in the application of me- 
chanical principles with which the mathematical student is 
but too familiar, where, when the data are before him, and 
the numerical and geometrical relations of his problems all 
clear to his conception — when his forces are estimated and 
his lines measured — nay, when even he has followed up the 
application of his technical processes, and fairly arrived at 
his conclusion — there is still something wanting in his mind 
— not in the evidence, for he has examined each link, and 
finds the chain complete — not in the principles, for those he 
well knows are too firmly established to be shaken — but 
precisely in the mode of action. He has followed out a train 
of reasoning by logical and technical rules, but the signs he 
has employed are not pictures of nature, or have lost their 
original meaning as such to his mind: he has not seen, as 
it were, the process of nature passing under his eye in an 
instant of time, and presented as a consecutive whole to his 
imagination. A familiar parallel, or an illustration drawn 



INTRODUCTION 29 

from some artificial or natural process, of which he has that 
direct and individual impression which gives it a reality and 
associates it with a name, will, in almost every such case, 
supply in a moment this deficient feature, will convert all 
his symbols into real pictures, and infuse an animated mean- 
ing into what was before a lifeless succession of words and 
signs. I cannot, indeed, always promise myself to attain 
this degree of vividness of illustration, nor are the points 
to be elucidated themselves always capable of being so 
paraphrased (if I may use the expression) by any single 
instance adducible in the ordinary course of experience ; but 
the object will at least be kept in view ; and, as I am very 
conscious of having, in making such attempts, gained for 
myself much clearer views of several of the more concealed 
effects of planetary perturbation than I had acquired by 
their mathematical investigation in detail, it may reason- 
ably be hoped that the endeavor will not always be unat- 
tended with a similar success in others. 

(10.) From what has been said, it will be evident that 
our aim is not to offer to the public a technical treatise, in 
which, the student of practical or theoretical astronomy shall 
find consigned the minute description of methods of obser- 
vation, or the formulas he requires prepared to his hand, or 
their demonstrations drawn out in detail. In all these the 
present work will be found meagre, and quite inadequate 
to his wants. Its aim is entirely different; being to present 
to him in each case the mere ultimate rationale of facts, 
arguments, and processes; and, in all cases of mathematical 
application, avoiding whatever would tend to encumber its 
pages with algebraic or geometrical symbols, to place under 
his inspection that central thread of common- sense on which 
the pearls of analytical research are invariably strung; but 



30 OUTLINES OF ASTRONOMY 

which, by the attention the latter claim for themselves, is 
often concealed "from the eye of the gazer, and not always 
disposed in the straightest and most convenient form to fol- 
low by those who string them. This is no fault of those 
who have conducted the inquiries to which we allude. The 
contention of mind for which they call is enormous ; and it 
may, perhaps, be owing to their experience of how little can 
be accomplished in carrying such processes on to their con- 
clusion, by mere ordinary clearness of head; and how neces- 
sary it often is to pay more attention to the purely mathe- 
matical conditions which insure success — the hooks-and-eyes 
of their equations and series — than to those which enchain 
causes with their effects, and both with the human reason — 
that we must attribute something of that indistinctness of 
view which is often complained of as a grievance by the 
earnest student, and still more commonly ascribed ironically 
to the native cloudiness of an atmosphere too sublime for 
vulgar comprehension. We think we shall render good 
service to both classes of readers, by dissipating, so far as 
lies in our power, that accidental obscurity, and by showing 
ordinary untutored comprehension clearly what it can, and 
what it cannot, hope to attain. 

(10 a.) To conclude: "Eome was not built in a day." 
No grand practical result of human industry, genius, or 
meditation, has sprung forth entire and complete from the 
master hand or mind of an individual designer working 
straight to its object, and foreseeing and providing for all 
details. As in the building of a great city, so in every such 
product, its historian has to record rude beginnings, circui- 
tous and inadequate plans; frequent demolition, renewal and 
rectification ; the perpetual removal of much cumbrous and 
unsightly material and scaffolding, and constant opening out 



INTRODUCTION 31 

of wider and grander conceptions; till at length a unity and 
a nobility is attained, little dreamed of in the imagination 
of the first projector. 

(10 b.) The same is equally true of every great body of 
knowledge, and would be found signally exemplified in the 
history of astronomy, did the object of this work allow us 
to devote a portion of it to its relation. What concerns us 
more is, that the same remark is no less applicable to the 
process by which knowledge is built up in the mind of each 
individual, and by which alone it can attain any extensive 
development or any grand proportions. No man can rise 
from ignorance to anything deserving to be called a com- 
plete grasp of any considerable branch of science without 
receiving and discarding in succession many crude and in- 
complete notions, which so far from injuring the truth in its 
ultimate reception, act as positive aids to its attainment by 
acquainting him with the symptoms of an insecure footing 
in his progress. To reach from the plain the loftiest sum- 
mits of an Alpine country, many inferior eminences have 
to be scaled and relinquished; but the labor is not lost. 
The region is unfolded in its closer recesses, and the grand 
panorama which opens from aloft is all the better under- 
stood and the more enjoyed for the very misconceptions in 
detail which it rectifies and explains. 

(10 c.) Astronomy is very peculiarly in this predicament. 
Its study to each individual student is a continual process 
of rectification and correction — of abandoning one point of 
view for another higher and better — for temporary and oc- 
casional reception of even positive and admitted errors for 
the convenience they afford toward giving clear notions of 
important truths whose essence they do, not affect, by spar- 
ing him that contention of mind which fatigues and dis- 



32 OUTLINES OF ASTRONOMY 

tresses. We know, for example, that the earth's diurnal 
motion is real, and that of the heavens only apparent; yet 
there are many problems in astronomy which are not only 
easier conceived, hut more simply resolved by adopting the 
idea of a diurnal rotation of the heavens, it being under- 
stood once for all that appearances are alike in both sup- 
positions. 



CHAPTER I 

General Notions — Apparent and real Motions — Shape and Size of the Earth 
— The Horizon and its Dip — The Atmosphere — Refraction — Twilight — 
Appearances resulting from Diurnal Motion — From Change of Station 
in General — Parallactic Motions — Terrestrial Parallax — That of the 
Stars Insensible — First Step toward forming an Idea of the Distance 
of the Stars — Copernican View of the Earth's Motion — Relative Mo- 
tion — Motions partly Real, partly Apparent — Geocentric Astronomy, 
or Ideal Reference of Phenomena to the Earth's Centre as a Common 
Conventional Station 

(11.) The magnitudes, distances, arrangement, and mo- 
tions of the great bodies which make up the vis.ble uni- 
verse, their constitution and physical condition, so far as 
they can be known to us, with their mutual influences 
and actions on each other, so far as they can be traced by 
the effects produced, and established by legitimate reason- 
ing, form the assemblage of objects to which the attention 
of the astronomer is directed. The term astronomy 1 itself, 
which denotes the law or rule of the astra (by which the 
ancients understood not only the stars properly so called, 
but the sun, the moon, and all the visible constituents of 
the heavens), sufficiently indicates this; and, although the 

i Ao-ttjp, a star ; vojuos, a law ; or ve^eiv, to tend, as a shepherd his flock ; so 
that ao-rpovoMos means "shepherd of the stars." The two etymologies are, 
however, coincident. 



OUTLINES OF ASTRONOMY 33 

term astrology, which, denotes the reason, theory, or inter- 
pretation of the stars, 3 has become degraded in its applica- 
tion, and confined to superstitious and delusive attempts 
to divine future events by their dependence on pretended 
planetary influences, the same meaning originally attached 
itself to that epithet. 

(12.) But, besides the stars and other celestial bodies, 
the earth itself, regarded as an individual body, is one prin- 
cipal object of the astronomer's consideration, and, indeed, 
the chief of all. It derives its importance, in a practical as 
well as theoretical sense, not only from its proximity, and 
its relation to us as animated beings, who draw from it the 
supply of all our wants, but as the station from which 
we see all the rest, and as the only one among them to 
which we can, in the first instance, refer for any deter- 
minate marks and measures by which to recognize their 
changes of situation, or with which to compare their 
distances. 

(13.) To the reader who now for the first time takes up 
a book on astronomy, it will no doubt seem strange to class 
the earth with the heavenly bodies, and to assume any com- 
munity of nature among things apparently so different. For 
what, in fact, can be more apparently different than the vast 
and seemingly immeasurable extent of the earth, and the 
stars, which appear but as points, and seem to have no size 
at all? The earth is dark and opaque, while the celestial 
bodies are brilliant. We perceive in it no motion, while in 
them we observe a continual change of place, as we view 
them at different hours of the day or night, or at different 
seasons of the year. The ancients, accordingly, one or two 

2 Aoyos, reason, or a word, the vehicle of reason ; the interpreter of thought. 



34 OUTLINES OF ASTRONOMY 

of the more enlightened of them only excepted, admitted 
no such community of nature; and, by thus placing the 
heavenly bodies and their movements without the pale of 
analogy and experience, effectually intercepted the progress 
of all reasoning from what passes here below, to what is 
going on in the regions where they exist and move. Under 
such conventions, astronomy, as a science of cause and 
effect, could not exist, but must be limited to a mere 
registry of appearances, unconnected with any attempt to 
account for them on reasonable principles, however suc- 
cessful to a certain extent might be the attempt to follow 
out their order of sequence, and to establish empirical laws 
expressive of this order. To get rid of this prejudice, there- 
fore, is the first step toward acquiring a knowledge of what 
is really the case; and the student has made his first effort 
toward the acquisition of sound knowledge, when he has 
learned to familiarize himself with the idea that the earth, 
after all, may be nothing but a great star. How correct 
such an idea may be, and with what limitations and modi- 
fications it is to be admitted, we shall see presently. 

(14.) It is evident, that, to form any just notions of the 
arrangement, in space, of a number of objects which we 
cannot approach and examine, but of which all the informa- 
tion we can gain is by sitting still and watching their evolu- 
tions, it must be very important for us to know, in the first 
instance, whether what we call sitting still is really such: 
whether the station from which we view them, with our- 
selves, and all objects which immediately surround us, be 
not itself in motion, unperceived by us ; and if so, of what 
nature that motion is. The apparent places of a number 
of objects, and their apparent arrangement with respect to 
each other, will of course be materially dependent on the 



OUTLINES OF ASTRONOMY 35 

situation of the spectator among them ; and if this situation 
be liable to change, unknown to the spectator himself, an 
appearance of change in the respective situations of the 
objects will arise, without the reality. If, then, such be 
actually the case, it will follow that all the movements we 
think we perceive among the stars will not be real move- 
ments, but that some part, at least, of whatever changes of 
relative place we perceive among them must be merely ap- 
parent, the results of the shifting of our own point of view; 
and that, if we would ever arrive at a knowledge of their 
real motions, it can only be by first investigating our own, 
and making due allowance for its effects. Thus, the ques- 
tion whether the earth is in motion or at rest, and if in 
motion, what that motion is, is no idle inquiry, but one on 
which depends our only chance of arriving at true conclu- 
sions respecting the constitution of the universe. 

(15.) Nor let it be thought strange that we should speak 
of a motion existing in the earth, unperceived by its inhabi- 
tants : we must remember that it is of the earth as a whole 
with all that it holds within its substance, or sustains on 
its surface, that we are speaking; of a motion common to 
the solid mass beneath, to the ocean which flows around 
it, the air that rests upon it, and the clouds which float 
above it in the air= Such a motion, which should displace 
no terrestrial object from its relative situation among others, 
interfere with no natural processes, and produce no sensa- 
tions of shocks or jerks, might, it is very evident, subsist 
undetected by us. There is no. peculiar sensation which 
advertises us that we are in motion. We perceive jerks, 
or shocks, it is true, because these are sudden changes of 
motion, produced, as the laws of mechanics teach us, by 
sudden and powerful forces acting during short times; and 



36 OUTLINES OF ASTRONOMY 

these forces, applied to our bodies, are what we feel. 
When, for example, we are carried along in a carriage 
with the blinds down, or with our eyes closed (to keep us 
from seeing external objects), we perceive a tremor arising 
from inequalities in the road, over which the carriage is 
successively lifted and let fall, but we have no sense of 
progress. As the road is smoother, our sense of motion 
is diminished, though our rate of travelling is accelerated. 
Bailway travelling, especially by night or in a tunnel, has 
familiarized every one with this remark. Those who have 
made aeronautic voyages testify that with closed eyes, and 
under the influence of a steady breeze communicating no 
oscillatory or revolving motion to the car, the sensation is 
that of perfect rest, however rapid the transfer from place 
to place. 

(16.) But it is on shipboard, where a great system is 
maintained in motion, and where we are surrounded with 
a multitude of objects which participate with ourselves and 
each other in the common progress of the whole mass, that 
we feel most satisfactorily the identity of sensation between 
a state of motion and one of rest. In the cabin of a large 
and heavy vessel, going smoothly before the wind in still 
water, or drawn along a canal, not the smallest indication 
acquaints us with the way it is making. We read, sit, walk, 
and perform every customary action as if we were on land. 
If we throw a ball into the air, it falls back into our hand; 
or if we drop it, it alights at our feet. Insects buzz around 
us as in the free air ; and smoke ascends in the same manner 
as it would do in an apartment on shore. If, indeed, we 
come on deck, the case is, in some respects, different; the 
air, not being carried along with us, drifts away smoke and 
other light bodies — such as feathers abandoned to it — appar- 



OUTLINES OF ASTRONOMY 37 

ently, in the opposite direction to that of the ship's prog- 
ress ; but, in reality, they remain at rest, and we leave them 
behind in the air. Still, the illusion, so far as massive ob- 
jects and our own movements are concerned, remains com- 
plete; and when we look at the shore, we then perceive 
the effect of our own motion transferred, in a contrary 
direction, to external objects — external, that is, to the system 
of which we form a part. 

"Provehimur portu, terraeque urbesque recedunt.'* 

(17.) In order, however, to conceive the earth as in 
motion, we must form to ourselves a conception of its 
shape and size. Now, an object cannot have shape and 
size unless it is limited on all sides by some definite out- 
line, so as to admit of our imagining it, at least, discon- 
nected from other bodies, and existing insulated in space. 
The first rude notion we form of the earth is that of a flat 
surface, of indefinite extent in all directions from the spot 
where we stand, above which are the air and sky ; below, to 
an indefinite profundity, solid matter. This is a prejudice 
to be got rid of, like that of the earth's immobility — but it 
is one much easier to rid ourselves of, inasmuch as it origi- 
nates only on our own mental inactivity, in not questioning 
ourselves where we will place a limit to a thing we have 
been accustomed from infancy to regard, as immensely large ; 
and does not, like that, originate in the testimony of our 
senses unduly interpreted. On the contrary, the direct 
testimony of our senses lies the other way. When we see 
the sun set in the evening in the west, and rise again 
in the east, as we cannot doubt that it is the same sun we 
see after a temporary absence, we must do violence to all 
our notions of solid matter, to suppose it to have made its 



38 OUTLINES OF ASTRONOMY 

way through the substance of the earth. It must, therefore, 
have gone under it, and that not by a mere subterraneous 
channel; for if we notice the points where it sets and rises 
for many successive days, or for a whole year, we shall find 
them constantly shifting, round a very large extent of the 
horizon; and, besides, the moon and stars also set and rise 
again in all points of the visible horizon. The conclusion 
is plain: the earth cannot extend indefinitely in depth 
downward, nor indefinitely in surface laterally; it must 
have not only bounds in a horizontal direction, but also 
an under side round which the sun, moon, and stars can 
pass; and that side must, at least, be so far like what we 
see, that it must have a sky and sunshine, and a day when 
it is night to us, and vice versa; where, in short, 

— "redit a nobis Aurora, diemque reducit. 
Nosque ubi primus equis oriens afflavit anhelis, 
Illic sera rubens accendit lumina Vesper." — Georg. 

(18.) As soon as we have familiarized ourselves with the 
conception of an earth without foundations or fixed sup- 
ports — existing insulated in space from contact of every 
thing external, it becomes easy to imagine it in motion — 
or, rather, difficult to imagine it otherwise; for, since there 
is nothing to retain it in one place, should any causes of 
motion exist, or any forces act upon it, it must obey their 
impulse. Let us next see what obvious circumstances there 
are to help us to a knowledge of the shape of the earth. 

(19.) Let us first examine what we can actually see of its 
shape. Now, it is not on land (unless, indeed, on uncom- 
monly level and extensive plains), that we can see anything 
of the general figure of the earth. The hills, trees, and other 
objects which roughen its surface, and break and elevate the 



OUTLINES OF ASTRONOMY M 

line of the horizon, though obviously bearing a most minute 
proportion to the whole earth, are yet too considerable with 
respect to ourselves and to that small portion of it which 
we can see at a single view, to allow of our forming any 
judgment of the form of the whole, from that of a part so 
disfigured. But with the surface of the sea or any vastly 
extended level plain, the case is otherwise. If we sail out 
of sight of land, whether we stand on the deck of the ship 
or climb the mast, we see the surface of the sea — not losing 
itself in distance and mist, but terminated by a sharp, clear, 
well-defined line or offing, as it is called, which runs all 
round us in a circle, having our station for its centre. 
That this line is really a circle, we conclude, first, from 
the perfect apparent similarity of all its parts; and, sec- 
ondly, from the fact of all its parts appearing at the same 
distance from us, and, that, evidently, a moderate one; and, 
thirdly, from this, that its apparent diameter, measured with 
an instrument called the dip sector, is the same (except 
under some singular atmospheric circumstances, which pro- 
duce a temporary distortion of the outline), in whatever 
direction the measure is taken — properties which belong 
only to the circle among geometrical figures. If we ascend 
a high eminence on a plain (for instance, one of the Egyp- 
tian pyramids), the same holds good. 

(20.) Masts of ships, however, and the edifices erected 
by man, are trifling eminences compared to what nature 
itself affords; ^Etna, Tenerifie, Mowna Eoa, are eminences 
from which no contemptible aliquot part of the whole earth's 
surface can be seen; but from these again — in those few and 
rare occasions when the transparency of the air will permit 
the real boundary of the horizon, the true sea-line, to be 
seen — the very same appearances are witnessed, but with 



40 OUTLINES OF ASTRONOMY 

this remarkable addition, viz., that the angular diameter of 
the visible area, as measured by the dip sector, is materially 
less than at a lower level; or, in other words, that the ap- 
parent size of the earth has sensibly diminished as we have 
receded from its surface, while yet the absolute quantity of 
it seen at once has been increased. 

(21.) The same appearances are observed universally, 
in every part of the earth's surface visited by man. Now, 
the figure of a body which, however seen, appears always 
circular, can be no other than a sphere or globe. 

(22.) A diagram will elucidate this. Suppose the earth 
to be represented by the sphere LHNQ, whose centre is 
C, and let A, Gr, M be stations at different elevations above 
various points of its surface, represented by a, g, m respect- 
ively. From each of them (as from M) let a line be drawn, 
as M N w, a tangent to the surface at N, then will this line 
represent the visual ray along which the spectator at M will 
see the visible horizon; and as this tangent sweeps round 
M, and comes successively into the positions M o, M P^>, 
M Q q, the point of contact N will mark out on the surface 
the circle NOPQ. The area of the spherical surface com- 
prehended within this circle is the portion of the earth's 
surface visible to a spectator at M, and the angle N M Q, 
included between the two extreme visual rays, is the meas- 
ure of its apparent angular diameter. Leaving, at present, 
out of consideration the effect of refraction in the air below 
M, of which more hereafter, and which always tends, in 
some degree, to increase that angle, or render it more obtuse, 
this is the angle measured by the dip sector. Now, it is 
evident, 1st, that as the point M is more elevated above m, 
the point immediately below it on the sphere, the visible 
area, i.e. the spherical segment or slice N P Q, increases; 



OUTLINES OF ASTRONOMY 



41 



2dly, that the distance of the visible horizon 3 or boundary 
of our view from the eye, viz., the line M N, increases; 
and, 3dly, that the angle N M Q becomes less obtuse, or, in 
other words, the apparent angular diameter of the earth 
diminishes, being nowhere so great as 180°, or two right 
angles, but falling short of it by some sensible quantity, 
and that more and more the higher we ascend. The figure 




exhibits three states or stages of elevation, with the horizon, 
etc., corresponding to each, a glance at which will explain 
our meaning ; or, limiting ourselves to the larger and more 
distinct, M N P Q, let the reader imagine wNM, M Q q 
to be the two legs of a ruler jointed at M, and kept extended 
by the globe NmQ between them. It is clear, that as the 
joint M is urged home toward the surface, the legs will 



'Opi£o> to terminate. 



42 OUTLINES OF ASTRONOMY 

open, and the ruler will become more nearly straight, but 
will not attain perfect straightness till M is brought fairly 
up to contact with, the surface at m, in which case its whole 
length will become a tangent to the sphere at m, as is the 
line x y. 

(23.) This explains what is meant by the dip of the hori- 
zon. M w, which is perpendicular to the general surface of 
the sphere at ra, is also the direction in which a plumb-line 4 
would hang ; for it is an observed fact, that in all situations, 
in every part of the earth, the direction of a plumb-line is 
exactly perpendicular to the surface of still water; and, 
moreover., that it is also exactly perpendicular to a line or 
surface truly adjusted by a spirit-level* Suppose, then, 
that at our station M we were to adjust a line (a wooden 
ruler, for instance) by a spirit-level, with perfect exactness; 
then, if we suppose the direction of this line indefinitely 
prolonged both ways, as X M Y, the line so drawn will be 
at right angles to M m, and therefore parallel to x m y } the 
tangent to the sphere at m. A spectator placed at M will 
therefore see not only all the vault of the sky above this 
line, as X Z Y, but also that portion or zone of it which 
lies between X N and Y Q; in other words, his sky will be 
more than a hemisphere by the zone YQXK It is the 
angular breadth of this redundant zone — the angle Y M Q, 
by which the visible horizon appears depressed below the 
direction of a spirit-level — that is called the dip of the hori- 
zon. It is a correction of constant use in nautical as- 
tronomy. 

(24.) From the foregoing explanations it appears, 1st, 
That the general figure of the earth (so far as it can be 

4 See these instruments described in Chap. III. 



OUTLINES OF ASTRONOMY 43 

gathered from this kind of observation) is that of a sphere 
or globe. In this we also include that of the sea, which, 
wherever it extends, covers and fills in those inequalities 
and local irregularities which exist on land, but which can 
of course only be regarded as trifling deviations from the 
general outline of the whole mass, as we consider an orange 
not the less round for the roughness on its rind. 2dly, That 
the appearance of a visible horizon, or sea-offing, is a conse- 
quence of the curvature of the surface, and does not arise 
from the inability of the eye to follow objects to a greater 
distance, or from atmospheric indistinctness. It will be 
worth while to pursue the general notion thus acquired into 
some of its consequences, by which its consistency with 
observations of a different kind, and on a larger scale, will 
be put to the test, and a clear conception be formed of the 
manner in which the parts of the earth are related to each 
other, and held together as a whole. 

(25.) In the first place, then, every one who has passed 
a little while at the seaside is aware that objects may be 
seen perfectly well beyond the offing or visible horizon — 
but not the whole of them. 
We only see their upper 
parts. Their bases where 
they rest on, or rise out 
of the water, are hid from 
view by the spherical sur- 
face of the sea, which pro- 
trudes between them and ourselves. Suppose a ship, for 
instance, to sail directly away from our station. At first, 
when the distance of the ship is small, a spectator, S, 
situated at some certain height above the sea, sees the 
whole of the ship, even to the vmter line where it rests on 




-^ 



44 OUTLINES OF ASTRONOMY 

the sea, as at A. As it recedes it diminishes, it is true, in 
apparent size, but still the whole is seen down to the water 
line, till it reaches the visible horizon at B. But as soon as 
it has passed this distance, not only does the visible por- 
tion still continue to diminish in apparent size, but the hull 
begins to disappear bodily, as if sunk below the surface. 
When it has reached a certain distance, as at C, its hull 
has entirely vanished, but the masts and sails remain, pre- 
senting the appearance c. But if, in this state of things, 
the spectator quickly ascends to a higher station, T, whose 
visible horizon is at D, the hull comes again in sight; and, 
when he descends again, he loses it. The ship still reced- 
ing, the lower sails seem to sink below the water, as at d, 
and at length the whole disappears: while yet the distinct- 
ness with which the last portion of the sail d is seen is such 
as to satisfy us that were it not for the interposed segment 
of the sea, ABODE, the distance T E is not so great as 
to have prevented an equally perfect view of the whole. 

(26.) The history of aeronautic adventure affords a curi- 
ous illustration of the same principle. The late Mr. Sadler, 
the celebrated aeronaut, ascended on one occasion in a bal- 
loon from Dublin, and was wafted across the Irish Channel, 
when, on his approach to the Welsh coast, the balloon de- 
scended nearly to the surface of the sea. By this time the 
sun was set, and the shades of evening began to close in. 
He threw out nearly all his ballast, and suddenly sprang 
upward to a great height, and by so doing brought his hori- 
zon to dip below the sun, producing the whole phenomenon 
of a western sunrise. M. Charles in his memorable ascent 
from Paris in 1783 witnessed the same phenomenon. 

(27.) If we could measure the heights and exact distance 
of two stations which could barely be discerned from each 




OUTLINES OF ASTRONOMY 45 

other over the edge of the horizon, we could ascertain the 
actual size of the earth itself: and, in fact, were it not for 
the effect of refraction, by which we are enabled to see in 
some small degree round the interposed segment (as will be 
hereafter explained), this would be a tolerably good method 
of ascertaining it. Suppose A and B to be two eminences, 
whose perpendicular heights A a and B b (which, for sim- 
plicity, we will suppose to be exactly equal) are known, as 
well as their exact horizontal in- 
terval a D b, by measurement; 
then it is clear that D, the visi- 
ble horizon of both, will lie just 
half-way between them, and if 
we suppose a D b to be the 
sphere of the earth, and C its centre in the figure 
C D b B, we know D b ) the length of the arch of the 
circle between D and b — viz., half the measured interval, 
and b B, the excess of its secant above its radius — which 
is the height of B — data which, by the solution of an easy 
geometrical problem, enable us to find the length of the 
radius D C. If, as is really the case, we suppose both the 
heights and distance of the stations inconsiderable in com- 
parison with the size of the earth, the solution alluded to 
is contained in the following proposition: 

The earth's diameter bears the same proportion to the dis- 
tance of the visible horizon from the eye as that distance does 
to the height of the eye above the sea level. 

When the stations are unequal in height, the problem 
is a little more complicated. 

(28.) Although, as we have observed, the effect of re- 
fraction prevents this from being an exact method of ascer- 
taining the dimensions of the earth, yet it will suffice to 



46 OUTLINES OF ASTRONOMY 

afford such, an approximation to it as shall be of use in the 
present stage of the reader's knowledge, and help him to 
many just conceptions, on which account we shall exemplify 
its application in numbers. Now, it appears by observation, 
that two points, each ten feet above the surface, cease to 
be visible from each other over still water, and in average 
atmospheric circumstances, at a distance of about 8 miles. 
But 10 feet is the 528th part of a mile, so that half that 
distance, or 4 miles, is to the height of each as 4x528 or 
2112 : 1, and therefore in the same proportion to 4 miles 
is the length, of the earth's diameter. It must, therefore, 
be equal to 4x2112 = 8448, or, in round numbers, about 
8000 miles, which is not very far from the truth. 

(29.) Such is the first rough result of an attempt to 
ascertain the earth's magnitude; and it will not be amiss, 
if we take advantage of it to compare it with objects we 
have been accustomed to consider as of vast size, so as 
to interpose a few steps between it and our ordinary ideas 
of dimension. We have before likened the inequalities 
on the earth's surface, arising from mountains, valleys, 
buildings, etc., to the roughnesses on the rind of an orange, 
compared with, its general mass. The comparison is quite 
free from exaggeration. The highest mountain known 
hardly exceeds five miles in perpendicular elevation: this 
is only one 1600th part of the earth's diameter; conse- 
quently, on a globe of sixteen inches in diameter, such 
a mountain would be represented by a protuberance of no 
more than one hundredth part of an inch, which is about 
the thickness of ordinary drawing-paper. Now, as there 
is no entire continent, or even any very extensive tract of 
land, known, whose general elevation above the sea is any- 
thing like half this quantity, it follows, that if we would 



OUTLINES OF ASTRONOMY 47 

construct a correct model of our earth, with its seas, con- 
tinents, and mountains, on a globe sixteen inches in diam- 
eter, the whole of the land, with the exception of a few 
prominent points and ridges, must be comprised on it 
within the thickness of thin writing-paper; and the highest 
hills would be represented bj the smallest visible grains 
of sand. 

(30.) The deepest mine existing does not penetrate half 
a mile below the surface: a scratch, or pin-hole, duly rep- 
resenting it, on the surface of such a globe as our model, 
would be imperceptible without a magnifier. 

(31.) The greatest depth of sea, probably, does not very 
much exceed the greatest elevation of the continents; and 
would, of course, be represented by an excavation, in about 
the same proportion, into the substance of the globe: so that 
the ocean comes to be conceived as a mere film of liquid, 
such as, on our model, would be left by a brush dipped in 
color, and drawn over those parts intended to represent the 
sea; only, in so conceiving it, we must bear in mind that 
the resemblance extends no further than to proportion in 
point of quantity. The mechanical laws which would reg- 
ulate the distribution and movements of such a film, 
and its adhesion to the surface, are altogether different from 
those which govern the phenomena of the sea. 

(32.) Lastly, the greatest extent of the earth's surface 
which has ever been brought at once within the range of 
human vision was that which, but for clouds, would have 
been exposed to the view of Messrs. Grlaisher and Coxwell, 
in their balloon ascent of September 5, 1863, to the enor- 
mous height of seven miles. To estimate the proportion 
of the area visible from this elevation to the whole earth's 
surface, we must have recourse to the geometry of the 



48 OUTLINES OF ASTRONOMY 

sphere, which, informs us that the convex surface of a 
spherical segment is to the whole surface to which it be- 
longs as the thickness of the segment is to the diameter 
of the sphere; and further, that this thickness, in the case 
we are considering, is almost exactly equal to the perpen- 
dicular elevation of the point of sight above the surface. 
The proportion, therefore, of the visible area, in this case, 
to the whole earth's surface, is that of seven miles to 8000, 
or 1 to 1140. The portion visible from iEtna, the Peak of 
Teneriffe, or Mowna Koa, is about one 4000th. 

(33.) When we ascend to any very considerable eleva- 
tion above the surface of the earth, either in a balloon, or 
on mountains, we are made aware, by many uneasy sensa- 
tions, of an insufficient supply of air. The barometer, an 
instrument which informs us of the weight of air incumbent 
on a given horizontal surface, confirms this impression, and 
affords a direct measure of the rate of diminution of the 
quantity of air which a given space includes as we recede 
from the surface. From its indications we learn, that when 
we have ascended to the height of 1000 feet, we have left 
below us about one- thirtieth of the whole mass of the atmos- 
phere — that at 10,600 feet of perpendicular elevation (which 
is rather less than that of the summit of -/Etna 6 ) we have 
ascended through about one- third; and at 18,000 feet (which 
is nearly that of Cotopaxi) through one- half the material, 
or, at least, the ponderable body of air incumbent on the 
earth's surface. From the progression of these numbers, 
as well as, a priori, from the nature of the air itself, which 
is compressible, i.e. capable of being condensed or crowded 



5 The height of ^tna above the Mediterranean (as it results from a baro- 
metrical measurement of my own, made in July, 1824, under very favorable 
circumstances) is 10,872 English feet. — Author. 



OUTLINES OF ASTRONOMY 49 

into a smaller space in proportion to the incumbent press- 
ure, it is easy to see that, although by rising still higher, 
we should continually get above more and more of the air, 
and so relieve ourselves more and more from the pressure 
with which it weighs upon us, yet the amount of this addi- 
tional relief, or the ponderable quantity of air surmounted, 
would be by no means in proportion to the additional height 
ascended, but in a constantly decreasing ratio. An easy 
calculation, however, founded on our experimental knowl- 
edge of the properties of air, and the mechanical laws which 
regulate its dilatation and compression, is sufficient to show 
that, at an altitude above the surface of the earth not ex- 
ceeding the hundredth part of its diameter, the tenuity, or 
rarefaction, of the air must be so excessive, that not only 
animal life could not subsist, or combustion be maintained 
in it, but that the most delicate means we possess of ascer- 
taining the existence of any air at all would fail to afford 
the slightest perceptible indications of its presence. 

(34.) Laying out of consideration, therefore, at present, 
all nice questions as to the probable existence of a definite 
limit to the atmosphere, beyond which there is, absolutely 
and rigorously speaking, no air, it is clear, that, for all 
practical purposes, we may speak of those regions which 
are more distant above the earth's surface than the hun- 
dredth part of its diameter as void of air, and of course of 
clouds (which are nothing but visible vapors, diffused and 
floating in the air, sustained by it, and rendering it turbid 
as mud does water). It seems probable, from many indica- 
tions, that the greatest height at which visible clouds ever 
exist does not exceed ten miles; at which height the density 
of the air is about an eighth part of what it is at the level 

of the sea. 

Astronomy — Vol. XIX.— 3 



50 OUTLINES OF ASTRONOMY 

(35.) We are thus led to regard the atmosphere of air, 
with the clouds it supports, as constituting a coating of 
equable or nearly equable thickness, enveloping our globe 
on all sides ; or rather as an aerial ocean, of which the sur- 
face of the sea and land constitutes the bed, and whose in- 
ferior portions or strata, within a few miles of the earth, 
contain by far the greater part of the whole mass, the den- 
sity diminishing with extreme rapidity as we recede upward, 
till, within a very moderate distance (such as would be rep- 
resented by the sixth of an inch on the model we have be- 
fore spoken of, and which is not more in proportion to the 
globe on which it rests, than the downy skin of a peach 
in comparison with the fruit within it), all sensible trace 
of the existence of air disappears. 

(36.) Arguments, however, are not wanting to render it, 
if not absolutely certain, at least in the highest degree prob- 
able, that the surface of the aerial, like that of the aqueous 
ocean, has a real and definite limit, as above hinted at; be- 
yond which there is positively no air, and above which a 
fresh quantity of air, could it be added from without, or 
carried aloft from below, instead of dilating itself indefi- 
nitely upward, would, after a certain very enormous but 
still finite enlargement of volume, sink and merge, as water 
poured into the sea, and distribute itself among the mass 
beneath. With the truth of this conclusion, however, as- 
tronomy has little concern; all the effects of the atmosphere 
in modifying astronomical phenomena being the same, 
whether it be supposed of definite extent or not. 

(37.) Moreover, whichever idea we adopt, within those 
limits in which it possesses any appreciable density its con- 
stitution is the same over all points of the earth's surface; 
that is to say, on the great scale, and leaving out of con- 



OUTLINES OF ASTRONOMY 51 

sideration temporary and local causes of derangement, such 
as winds, and great fluctuations, of the nature of waves, 
which prevail in it to an immense extent. In other words, 
the law of diminution of the air's density as we recede up- 
ward from the level of the sea is the same in every column 
into which we may conceive it divided, or from whatever 
point of the surface we may set out. It may therefore be 
considered as consisting of successively superposed strata 
or layers, each of the form of a spherical shell, concentric 
with the general surface of the sea and land, and each of 
which is rarer, or specifically lighter, than that immediately 
beneath it; and denser, or specifically heavier, than that im- 
mediately above it. This, at least, is the kind of distribu- 
tion which alone would be consistent with the laws of the 
equilibrium of fluids. Inasmuch, however, as the atmos- 
phere is not in perfect equilibrium, being always kept in 
a state of circulation, owing to the excess of heat in its 
equatorial regions over that at the poles, some slight devia- 
tion from the rigorous expression of this law takes place, 
and in peculiar localities there is reason to believe that even 
considerable permanent depressions of the contours of these 
strata, below their general or spherical level, subsist. But 
these are points of consideration rather for the meteorologist 
than the astronomer. It must be observed, moreover, that 
with this distribution of its strata the inequalities of moun- 
tains and valleys have little concern. These exercise hardly 
more influence in modifying their general spherical figure 
than the inequalities at the bottom of the sea interfere with 
the general sphericity of its surface. They would exercise 
absolutely none were it not for their effect in giving another 
than horizontal direction to the currents of air constituting 
winds, as shoals in the ocean throw up the currents which 



52 OUTLINES OF ASTRONOMY 

sweep over them toward the surface, and so in some small 
degree tend to disturb the perfect level of that surface. 

(38.) It is the power which air possesses, in common 
with all transparent media, of refracting the rays of light, 
or bending them out of their straight course, which renders 
a knowledge of the constitution of the atmosphere important 
to the astronomer. Owing to this property, objects seen 
obliquely through it appear otherwise situated than they 
would to the same spectator, had the atmosphere no exist- 
ence. It thus produces a false impression respecting their- 
places, which must be rectified by ascertaining the amount 
and direction of the displacement so apparently produced 
on each, before we can come at a knowledge of the true 
directions in which they are situated from us at any assigned 
moment. 

(39.) Suppose a spectator placed at A, any point of the 
earth's surface KA^; and let LI, M »i, N w, represent the 
successive strata or layers, of decreasing density, into which 
we may conceive the atmosphere to be divided, and which 
are spherical surfaces concentric with K &, the earth's sur- 
face. Let S represent a star, or other heavenly body, be- 
yond the utmost limit of the atmosphere. Then, if the air 
were away, the spectator would see it in the direction of the 
straight line A S. But, in reality, when the ray of light 
S A reaches the atmosphere, suppose at d, it will, by the 
laws of optics, begin to bend downward, and take a more 
inclined direction, as d c. This bending will at first be im- 
perceptible, owing to the extreme tenuity of the uppermost 
strata; but as it advances downward, the strata continually 
increasing in density, it will continually undergo greater 
and greater refraction in the same direction; and thus, in- 
stead of pursuing the straight line S d A, it will describe a 



OUTLINES OF ASTRONOMY 



53 



curve S d c b a, continually more and more concave down- 
ward, and will reach the earth, not at A, but at a certain 
point a, nearer to S. This ray, consequently, will not reach 
the spectator's eye. The ray by which he will see the star 
is, therefore, not SdA, but another ray which, had there 
been no atmosphere, would have struck the earth at K, a 
point behind the spectator; but which, being bent by the air 
into the curve S D C B A, actually strikes on A. Now, it 




is a law of optics, that an object is seen in the direction 
which the visual ray has at the instant of arriving at the 
eye, without regard to what may have been otherwise its 
course between the object and the eye. Hence the star S 
will be seen, not in the direction A S, but in that of A s, 
a tangent to the curve S D C B A, at A. But because the 
curve described by the refracted ray is concave downward, 
the tangent A s will lie above A S, the unrefracted ray: 
consequently the object S will appear more elevated above 



54 OUTLINES OF ASTRONOMY 

the horizon A H, when seen through the refracting atmos- 
phere, than it would appear were there no such atmosphere. 
Since, however, the disposition of the strata is the same in 
all directions around A, the visual ray will not be made to 
deviate laterally, but will remain constantly in the same 
vertical plane, S A C, passing through the eye, the object, 
and the earth's centre. 

(40.) The effect of the air's refraction, then, is to raise 
all the heavenly bodies higher above the horizon in appear- 
ance than they are in reality. Any such body, situated 
actually in the true horizon, will appear above it, or will 
have some certain apparent altitude (as it is called). Nay, 
even some of those actually below the horizon, and which 
would therefore be invisible but for the effect of refraction, 
are, by that effect, raised above it and brought into sight. 
Thus, the sun, when situated at P below the true horizon, 
A H, of the spectator, becomes visible to him, as if it 
stood at p, by the refracted ray P q r t A, to which A p 
is a tangent. 

(41.) The exact estimation of the amount of atmospheric 
refraction, or the strict determination of the angle S A 5, by 
which a celestial object at any assigned altitude, H A S, is 
raised in appearance above its true place, is, unfortunately, 
a very difficult subject of physical inquiry, and one on 
which geometers (from whom alone we can look for any 
information on the subject) are not yet entirely agreed. 
The difficulty arises from this, that the density of any 
stratum of air (on which its refracting power depends) is 
affected not merely by the superincumbent pressure, but 
also by its temperature or degree of heat. Now, although 
we know that as we recede from the earth's surface the 
temperature of the air is constantly diminishing, yet the 



OUTLINES OF ASTRONOMY 55 

law, or amount of this diminution at different heights, is 
not yet fully ascertained. Moreover, the refracting power 
of air is perceptibly affected by its moisture ; and this, too, 
is not the same in every part of an aerial column; neither 
are we acquainted with the laws of its distribution. The 
consequence of our ignorance on these points is to introduce 
a corresponding degree of uncertainty into the determina- 
tion of the amount of refraction, which affects, to a certain 
appreciable extent, our knowledge of several of the most 
important data of astronomy. The uncertainty thus in- 
duced is, however, confined within such very narrow limits 
as to be no cause of embarrassment, except in the most 
delicate inquiries, and to call for no further allusion in a 
treatise like the present. 

(42.) A "Table of Eefractions, " as it is called, or a 
statement of the amount of apparent displacement arising 
from this cause, at all altitudes, or in every situation of a 
heavenly body, from the horizon to the zenith* (or point 
of the sky vertically above the spectator), and under all 
the circumstances in which astronomical observations are 
usually performed which may influence the result, is one 
of the most important and indispensable of all astronomical 
tables, since it is only by the use of such a table we are en- 
abled to get rid of an illusion which must otherwise pervert 
all our notions respecting the celestial motions. Such have 
been, accordingly, constructed with great care, and are to 
be found in every collection of astronomical tables. Our 
design, in the present treatise, will not admit of the intro- 
duction of tables; and we must, therefore, content ourselves 



6 From an Arabic word of this signification. See this term technically 
defined in Chap. II. 



56 OUTLINES OF ASTRONOMY 

here, and in similar cases, with referring the reader to works 
especially destined to furnish these useful aids to calcula- 
tion. It is, however, desirable that he should bear in mind 
the following general notions of its amount, and law of 
variations. 

(43.) 1st. In the zenith there is no refraction. A celes- 
tial object, situated vertically overhead, is seen in its true 
direction, as if there were no atmosphere, at least if the air 
be tranquil. 

2dly. In descending from the zenith to the horizon, the 
refraction continually increases. Objects near the horizon 
appear more elevated by it above their true directions than 
those at a high altitude. 

3dly. The rate of its increase is nearly in proportion to 
the tangent of the apparent angular distance of the object 
from the zenith. But this rule, which is not far from the 
truth, at moderate zenith distances, ceases to give correct 
results in the vicinity of the horizon, where the law be- 
comes much more complicated in its expression. 

4thly. The average amount of refraction, for an object 
half-way between the zenith and horizon, or at an apparent 
altitude of 45°, is about 1' (more exactly, 57"), a quantity 
hardly sensible to the naked eye ; but at the visible horizon 
it amounts to no less a quantity than 33', which is rather 
more than the greatest apparent diameter of either the sun 
or the moon. Hence it follows, that when we see the lower 
edge of the sun or moon just apparently resting on the 
horizon, its whole disk is in reality below it, and would be 
entirely out of sight and concealed by the convexity of the 
earth, but for the bending round it, which the rays of light 
have undergone in their passage through the air, as alluded 
to in art. 40. 



OUTLINES OF ASTRONOMY 57 

5thly. That when the barometer is higher than its aver- 
age or mean state, the amount of refraction is greater than 
its mean amount; when lower, less: and, 

6thly. That for one and the same reading of the barome- 
ter the refraction is greater, the colder the air. The varia- 
tions, owing to these two causes, from its mean amount (at 
temp. 55°, pressure 30 inches), are about one 420th part of 
that amount for each degree of the thermometer of Fahren- 
heit, and one 300th for each tenth of an inch in the height 
of the barometer. 

(M.) It follows from this, that one obvious effect of 
refraction must be to shorten the duration of night and 
darkness, by actually prolonging the stay of the sun and 
moon above the horizon. But even after they are set, the 
influence of the atmosphere still continues to send us a por- 
tion of their light; not, indeed, by direct transmission, but 
by reflection upon the vapors and minute solid particles 
which float in it, and, perhaps, also on the actual material 
atoms of the air itself. To understand how this takes 
place, we must recollect, that it is not only by the direct 
light of a luminous object that we see, but that whatever 
portion of its light which would not otherwise reach our 
eyes is intercepted in its course, and thrown back, or lat- 
erally, upon us, becomes to us a means of illumination. 
Such reflective obstacles always exist floating in the air. 
The whole course of a sunbeam penetrating through the 
chink of a window- shutter into a dark room is visible as a 
bright line in the air: and even if it be stifled, or let out 
through an opposite crevice, the light scattered through the 
apartment from this source is sufficient to prevent entire 
darkness in the room. The luminous lines occasionally 
seen in the air, in a sky full of partially broken clouds, 



58 



OUTLINES OF ASTRONOMY 



which the vulgar term "the sun drawing water," are simi- 
larly caused. They are sunbeams, through apertures in 
clouds, partially intercepted and reflected on the dust and 
vapors of the air below. Thus it is with those solar rays 
which, after the sun is itself concealed by the convexity of 
the earth, continue to traverse the higher regions of the at- 
mosphere above our heads, and pass through and out of it, 
without directly striking on the earth at all. Some portion 
of them is intercepted and reflected by the floating particles 
above mentioned, and thrown back, or laterally, so as to 




reach us, and afford us that secondary illumination, which 
is twilight. The course of such rays will be immediately 
understood from the above figure, in which A B C D is the 
earth; A a point on its surface, where the sun S is in 
the act of setting: its last lower ray SAM just grazing the 
surface at A, while its superior rays S 1ST, S 0, traverse the 
atmosphere above A without striking the earth, leaving it 
finally at the points PQE, after being more or less bent in 
passing through it, the lower most, the higher less, and that 
which, like SEO, merely grazes the exterior limit of the 



OUTLINES OF ASTRONOMY 59 

atmosphere, not at all. Let us consider several points, A, 
B, C, D, each more remote than the last from A, and each 
more deeply involved in the earth's shadow, which occupies 
the whole space from A beneath the line A M. Now, 
A just receives the sun's last direct ray, and, besides, is 
illuminated by the whole reflective atmosphere P Q E T. 
It therefore receives twilight from the whole sky. The 
point B, to which the sun has set, receives no direct solar 
light, nor any, direct or reflected, from all that part of its 
visible atmosphere which is below A P M; but from the 
lenticular portion P Ex, which is traversed by the sun's 
rays, and which lies above the visible horizon B E of B, 
it receives a twilight, which is strongest at E, the point im- 
mediately below which the sun is, and fades away gradually 
toward P, as the luminous part of the atmosphere thins off. 
At C, only the last or thinnest portion, P Q z of the len- 
ticular segment, thus illuminated, lies above the horizon, 
C Q, of that place; here, then, the twilight is feeble, and 
confined to a small space in and near the horizon, which 
the sun has quitted, while at D the twilight has ceased 
altogether. 

(45.) When the sun is above the horizon, it illuminates 
the atmosphere and clouds, and these again disperse and 
scatter a portion of its light in all directions, so as to send 
some of its rays to every exposed point, from every point 
of the sky» The generally diffused light, therefore, which 
we enjoy in the daytime, is a phenomenon originating in 
the very same causes as the twilight. Were it not for the 
reflective and scattering power of the atmosphere, no objects 
would be visible to us out of direct sunshine ; every shadow 
of a passing cloud would be pitchy darkness; the stars 
would be visible all day, and every apartment, into which 



60 OUTLINES OF ASTRONOMY 

the sun had not direct admission, would be involved in noc- 
turnal obscurity. This scattering action of the atmosphere 
on the solar light, it should be observed, is increased by 
the irregularity of temperature caused by the same luminary 
in its different parts, which, during the daytime, throws it 
into a constant state of undulation, and, by thus bringing 
together masses of air of very unequal temperatures, pro- 
duces partial reflections and refractions at their common 
boundaries, by which some portion of the light is turned 
aside from the direct course, and diverted to the purposes 
of general illumination. A secondary twilight, however, 
may be traced even beyond the point D, consequent on a 
re- reflection of the rays dispersed through the atmosphere 
in the primary one. The phenomenon seen in the clear 
atmosphere of the Nubian desert, described by travellers 
under the name of the "After- glow," would seem to arise 
from this cause. 

(46.) From the explanation we have given, in arts. 39 
and 40, of the nature of atmospheric refraction, and the 
mode in which it is produced in the progress of a ray of 
light through successive strata, or layers, of the atmosphere, 
it will be evident, that whenever a ray passes obliquely from 
a higher level to a lower one, or vice versa, its course is not 
rectilinear, but concave downward; and of course any ob- 
ject seen by means of such a ray, must appear deviated 
from its true place, whether that object be, like the celestial 
bodies, entirely beyond the atmosphere, or, like the summits 
of mountains seen from the plains, or other terrestrial sta- 
tions at different levels seen from each other, immersed 
in it. Every difference of level, accompanied, as it must 
be, with a difference of density in the aerial strata, must 
also have, corresponding to it, a certain amount of refrac- 



OUTLINES OF ASTRONOMY 61 

tion ; less, indeed, than what would be produced" by the 
whole atmosphere, but still often of very appreciable, and 
even considerable, amount. This refraction between terres- 
trial stations is termed terrestrial refraction, to distinguish it 
from that total effect which is only produced on celestial 
objects, or such as are beyond the atmosphere, and which 
is called celestial or astronomical refraction. 

(47.) Another effect of refraction is to distort the visible 
forms and proportions of objects seen near the horizon. The 
sun, for instance, which at a considerable altitude always 
appears round, assumes, as it approaches the horizon, a 
flattened or oval outline; its horizontal diameter being 
visibly greater than that in a vertical direction. When 
very near the horizon, this flattening is evidently more 
considerable on the lower side than on the upper; so that 
the apparent form is neither circular nor elliptic, but a 
species of oval, which deviates more from a circle below 
than above. This singular effect, which any one may notice 
in a fine sunset, arises from the rapid rate at which the re- 
fraction increases in approaching the horizon. Were every 
visible point in the sun's circumference equally raised by 
refraction, it would still appear circular, though displaced; 
but the lower portions being more raised than the upper, 
the vertical diameter is thereby shortened, while the two 
extremities of its horizontal diameter are equally raised, 
and in parallel directions, so that its apparent length re- 
mains the same. The dilated size (generally) of the sun or 
moon, when seen near the horizon, beyond what they appear 
to have when high up in the sky, has nothing to do with 
refraction. It is an illusion of the judgment, arising from 
the terrestrial objects interposed, or placed in close com- 
parison with them. In that situation we view and judge of 



62 OUTLINES OF ASTRONOMY 

them as we do of terrestrial objects — in detail, and with 
an acquired habit of attention to parts. Aloft we have no 
associations to guide us, and their insulation in the expanse 
of sky leads us rather to undervalue than to overrate their 
apparent magnitudes. Actual measurement with a proper 
instrument corrects our error, without, however, dispelling 
our illusion. By this we learn, that the sun, when just on 
the horizon, subtends at our eyes almost exactly the same, 
and the moon a materially less angle, than when seen at a 
great altitude in the sky, owing to its greater distance from 
us in the former situation as compared with the latter, as 
will be explained further on. 

(48.) After what has been said of the small extent of 
the atmosphere in comparison with the mass of the earth, 
we shall have little hesitation in admitting those luminaries 
which people and adorn the sky, and which, while they 
obviously form no part of the earth, and receive no support 
from it, are yet not borne along at random like clouds upon 
the air, nor drifted by the winds, to be external to our 
atmosphere. As such we have considered them while 
speaking of their refractions — as existing in the immensity 
of space beyond, and situated, perhaps, for anything we can 
perceive to the contrary, at enormous distances from us and 
from .each other. 

(49.) Could a spectator exist unsustained by the earth, 
or any solid support, he would see around him at one view 
the whole contents of space — the visible constituents of the 
universe : and, in the absence of any means of judging of 
their distances from him, would refer them, in the directions 
in which they were seen from his station, to the concave 
surface of an imaginary sphere, having his eye for a centre, 
and its surface at some vast indeterminate distance. Per- 



OUTLINES OF ASTRONOMY 63 

haps "he might judge those which appear to him large and 
bright, to be nearer to him than the smaller and less bril- 
liant; but, independent of other means of judging, he would 
have no warrant for this opinion, any more than for the idea 
that all were equidistant from him, and really arranged on 
such a spherical surface. Nevertheless, there would be 
no impropriety in his referring their places, geometrically 
speaking, to those points of such a purely imaginary sphere, 
which their respective visual rays intersect; and there would 
be much advantage in so doing, as by that means their ap- 
pearance and relative situation could be accurately meas- 
ured, recorded, and mapped down. The objects in a land- 
scape are at every variety of distance from the eye, yet we 
lay them all down in a picture on one plane, and at one 
distance, in their actual apparent proportions, and the like- 
ness is not taxed with incorrectness, though a man in the 
foreground should be represented larger than a mountain 
in the distance. So it is to a spectator of the heavenly 
bodies pictured, projected, or mapped down on that imagi- 
nary sphere we call the shy or heaven. Thus, we may easily 
conceive that the moon, which appears to us as large as the 
sun, though less bright, may owe that apparent equality to 
its greater proximity, and may be really much less; while 
both the moon and sun may only appear larger and brighter 
than the stars, on account of the remoteness of the latter. 

(50.) A spectator on the earth's surface is prevented, by 
the great mass on which he stands, from seeing into all that 
portion of space which is below him, or to see which he 
must look in any degree downward. It is true that, if his 
place of observation be at a great elevation, the dip of the 
horizon will bring within the scope of vision a little more 
than a hemisphere, and refraction, wherever he may be 



64 OUTLINES OF ASTRONOMY 

situated, will enable him to look, as it were, a little round 
the corner; but the zone thus added to his visual range can 
hardly ever, unless in very extraordinary circumstances, 
exceed a couple of degrees in breadth, and is always ill 
seen on account of the vapors near the horizon. Unless, 
then, by a change of his geographical situation, he should 
shift his horizon (which is always a plane passing through 
his eye, and touching the spherical convexity of the earth); 
or unless, by some movements proper to the heavenly 
bodies, they should of themselves come above his horizon; 
or, lastly, unless, by some rotation of the earth itself on its 
centre, the point of its surface which he occupies should be 
carried round, and presented toward a different region of 
space; he would never obtain a sight of almost one-half 
the objects external to our atmosphere. But if any of these 
cases be supposed, more, or all, may come into view accord- 
ing to the circumstances. 

(51.) A traveller, for example, shifting his locality on 
our globe, will obtain a view of celestial objects invisible 
from his original station, in a way which may be not inaptly 
illustrated by comparing him to a person standing in a park 
close to a large tree. The massive obstacle presented by its 
trunk cuts off his view of all those parts of the landscape 
which it occupies as an object; but by walking round it a 
complete successive view of the whole panorama may be 
obtained. Just in the same way, if we set off from any 
station, as London, and travel southward, we shall not fail 
to notice that many celestial objects which are never seen 
from London come successively into view, as if rising up 
above the horizon, night after night, from the south, al- 
though it is in reality our horizon, which, travelling with 
us southward round the sphere, sinks in succession beneath 



OUTLINES OF ASTRONOMY 65 

them. The novelty and splendor of fresh constellations 
thus gradually brought into view in the clear calm nights 
of tropical climates, in long voyages to the south, is dwelt 
upon by all who have enjoyed this spectacle, and never 
fails to impress itself on the recollection among the most 







* 4f 



delightful and interesting of the associations connected with 
extensive travel. A glance at the accompanying figure, 
exhibiting three successive stations of a traveller, A, B, 0, 
with the horizon corresponding to each, will place this 
process in clearer evidence than any description. 

(52.) Again: suppose the earth itself to have a motion 
of rotation on its centre. It is evident that a spectator at 
rest (as it appears to him) on any part of it will, unper- 
ceived by himself, be carried round with it: unperceived, 
we say, because his horizon will constantly contain, and be 
limited by, the same terrestrial objects. He will have the 
same landscape constantly before his eyes, in which all 
the familiar objects in it, which serve him for landmarks 
and directions, retain, with respect to himself or to each 
other, the same invariable situations. The perfect smooth- 
ness and equality of the motion of so vast a mass, in which 
every object he sees around him participates alike, will (art. 



66 OUTLINES OF ASTRONOMY 

15) prevent his entertaining any suspicion of his actual 
change of place. Yet, with respect to external objects — 
that is to say, all celestial ones which do not participate 
in the supposed rotation of the earth — his horizon will have 
been all the while shifting in its relation to them, precisely 
as in the case of our traveller in the foregoing article. 
Kecurring to the figure of that article, it is evidently the 
same thing, so far as their visibility is concerned, whether 
he has been carried by the earth's rotation successively into 
the situations A, B, C ; or whether, the earth remaining at 
rest, he has transferred himself personally along its surface 
to those stations. Our spectator in the park will obtain 
precisely the same view of the landscape, whether he walk 
round the tree, or whether we suppose it sawed off, and 
made to turn on an upright pivot, while he stands on a 
projecting step attached to it, and allows himself to be 
carried round by its motion. The only difference will be 
in his view of the tree itself, of which, in the former case, 
he will see every part, but, in the latter, only that portion 
of it which remains constantly opposite to him, and imme- 
diately under his eye. 

(53.) By such a rotation of the earth, then, as we have 
supposed, the horizon of a stationary spectator will be con- 
stantly depressing itself below those objects which lie in 
that region of space toward which the rotation is carrying 
him, and elevating itself above those in the opposite quar- 
ter, admitting into view the former, and successively 'hiding 
the latter. As the horizon of every such spectator, how- 
ever, appears to him motionless, all such changes will be 
referred by him to a motion in the objects themselves so 
successively disclosed and concealed. In place of his hori- 
zon approaching the stars, therefore, he will judge the stars 



OUTLINES OF ASTRONOMY 67 

to approach his horizon ; and when it passes over and hides 
any of them, he will consider them as having sunk below 
it, or set; while those it has just disclosed, and from which 
it is receding, will seem to be rising above it. 

(54.) If we suppose this rotation of the earth to continue 
in one and the same direction — that is to say, to be per- 
formed round one and the same axis, till it has completed 
an entire revolution, and come back- to the position from 
which it set out when the spectator began his observations 
— it is manifest that everything will then be in precisely 
the same relative position as at the outset: all the heavenly 
bodies will appear to occupy the same places in the concave 
of the sky which they did at that instant, except such as 
may have actually moved in the interim; and if the rota- 
tion still continue, the same phenomena of their successive 
rising and setting, and return to the same places, will con- 
tinue to be repeated in the same order, and (if the velocity 
of rotation be uniform) in equal intervals of time, ad in- 
finitum. 

(55.) Now, in this we have a lively picture of that grand 
phenomenon, the most important beyond all comparison 
which nature presents, the daily rising and setting of the 
sun and stars, their progress through the vault of the heav- 
ens, and their return to the same apparent places at the 
same hours of the day and night. The accomplishment of 
this restoration in the regular interval of twenty- four hours 
is the first instance we encounter of that great law of perio- 
dicity, 7 which, as we shall see, pervades all astronomy; by 
which expression we understand the continual reproduction 
of the same phenomena, in the same order, at equal inter- 
vals of time. 



7 nepioSos, a going round, a circulation or revolution. 



68 OUTLINES OF ASTRONOMY 

(56.) A free rotation of the earth round its centre, if it 
exist and be performed in consonance with the same me- 
chanical laws which obtain in the motions of masses of mat- 
ter under our immediate control, and within our ordinary 
experience, must be such as to satisfy two essential condi- 
tions. It must be invariable in its direction with respect to 
the sphere itself, and uniform in its velocity. The rotation 
must be performed round an axis or diameter of the sphere, 
whose poles or extremities, where it meets the surface, cor- 
respond always to the same points on the sphere. Modes 
of rotation of a solid body under the influence of external 
agency are conceivable, in which the poles of the imaginary 
line or axis about which it is at any moment revolving shall 
hold no fixed places on the surface, but shift upon it every 
moment. Such changes, however, are inconsistent with the 
idea of a rotation of a body of regular figure about its axis 
of symmetry, performed in free space, and without resist- 
ance or obstruction from any surrounding medium, or dis- 
turbing influences. The complete absence of such obstruc- 
tions draws with it, of necessity, the strict fulfilment of the 
two conditions above mentioned. 

(57.) Now, these conditions are in perfect accordance 
with what we observe, and what recorded observation 
teaches us, in respect of the diurnal motions of the heav- 
enly bodies. We have no reason to believe, from history, 
that any sensible change has taken place since the earliest 
ages in the interval of time elapsing between two successive 
returns of the same star to the same point of the sky; or, 
rather, it is demonstrable from astronomical records that no 
such change has taken place. And with respect to the other 
condition — the permanence of the axis of rotation — the appear- 
ances which any alteration in that respect must produce, 



OUTLINES OF ASTRONOMY 69 

would be marked, as we shall presently show, by a corre- 
sponding change of a very obvious kind in the apparent 
motions of the stars; which, again, history decidedly de- 
clares them not to have undergone. 

(58.) But, before we proceed to examine more in detail 
how the hypothesis of the rotation of the earth about an 
axis accords with the phenomena which the diurnal motion 
of the heavenly bodies offers to our notice, it will be proper 
to describe, with precision, in what that diurnal motion 
consists, and how far it is participated in by them all; or 
whether any of them form exceptions, wholly or partially, 
to the common analogy of the rest. We will, therefore, 
suppose the reader to station himself, on a clear evening, 
just after sunset, when the first stars begin to appear, in 
some open situation whence a good general view of the 
heavens can be obtained. He will then perceive, above 
and around him, as it were, a vast concave hemispherical 
vault, beset with stars of various magnitudes, of which the 
brightest only will first catch his attention in the twilight; 
and more and more will appear as the darkness increases, 
till the whole sky is overspangled with them. When he 
has a while admired the calm magnificence of this glorious 
spectacle, the theme of so much song, and of so much 
thought — a spectacle which no one can view without emo- 
tion, and without a longing desire to know something of its 
nature and purport — let him fix his attention more particu- 
larly on a few of the most brilliant stars, such as he cannot 
fail to recognize again without mistake after looking away 
from them for some time, and let him refer their apparent 
situations to some surrounding objects, as buildings, trees, 
etc., selecting purposely such as are in different quarters of 
his horizon. On comparing them again with their respec- 



70 OUTLINES OF ASTRONOMY 

tive points of reference, after a moderate interval, as the 
night advances, he will not fail to perceive that they have 
changed their places, and advanced, as by a general move- 
ment, in a westward direction; those toward the eastern 
quarter appearing to rise or recede from the horizon, while 
those which lie toward the west will be seen to approach it; 
and, if watched long enough, will, for the most part, finally 
sink beneath it, and disappear; while others, in the eastern 
quarter, will be seen to rise as if out of the earth, and, join- 
ing in the general procession, will take their course with 
the rest toward the opposite quarter. 

(59.) If he persist for a considerable time in watching 
their motions, on the same or on several successive nights, 
he will perceive that each star appears to describe, as far as 
its course lies above the horizon, a circle in the sky; that 
the circles so described are not of the same magnitude for 
all the stars; and that those described by different stars 
differ greatly in respect of the parts of them which lie above 
the horizon. Some, which lie toward the quarter of the 
horizon which is denominated the South, ° only remain for 
a short time above it, and disappear, after describing in 
sight only the small upper segment of their diurnal circle; 
others, which rise between the south and east, describe 
larger segments of their circles above the horizon, remain 
proportionally longer in sight, and set precisely as far to 
the westward of south as they rose to the eastward; while 
such as rise exactly in the east remain just twelve hours 
visible, describe a semicircle, and set exactly in the west. 
With those, again, which rise between the east and north, 



8 We suppose our observer to be stationed in some northern latitude ; some- 
where in Europe, for example. 



OUTLINES OF ASTRONOMY 71 

the same law obtains; at least, as far as regards the time 
of their remaining above the horizon and the proportion of 
the visible segment of their diurnal circles to their whole 
circumferences. Both go on increasing; they remain in 
view more than twelve hours, and their visible diurnal arcs 
are more than semicircles. But the magnitudes of the cir- 
cles themselves diminish, as we go from the east, north- 
ward; the greatest of all the circles being described by 
those which rise exactly in the east point. Carrying his 
eye further northward, he will notice, at length, stars 
which, in their diurnal motion, just graze the horizon at 
its north point, or only dip below it for a moment; while 
others never reach it at all, but continue always above it, 
revolving in entire circles round one point called the pole, 
which appears to be the common centre of all their motions, 
and which alone, in the whole heavens, may be considered 
immovable. Not that this point is marked by any star. It 
is a purely imaginary centre; but there is near it one con- 
siderably bright star, called the Pole Star, which is easily 
recognized by the very small circle it describes; so small, 
indeed, that, without paying particular attention, and refer- 
ring its position very nicely to some fixed mark, it may 
easily be supposed at rest, and be, itself, mistaken for the 
common centre about which all the others in that region 
describe their circles; or it may be known by its configura- 
tion with a very splendid and remarkable constellation or 
group of stars, called by astronomers the Great Bear. 

(60.) He will further observe, that the apparent relative 
situations of all the stars among one another, is not changed 
by their diurnal motion. In whatever parts of their circles 
they are observed, or at whatever hour of the night, they 
form with each other the same identical groups or configu- 



72 OUTLINES OF ASTRONOMY 

rations, to which the name of constellations has been 
given. It is true, that, in different parts of their course, 
these groups stand differently with respect to the horizon; 
and those toward the north, when in the course of their 
diurnal movement they pass alternately above and below 
that common centre of motion described in the last article, 
become actually inverted with respect to the horizon, while, 
on the other hand, they always turn the same points toward 
the pole. In short, he will perceive that the whole assem- 
blage of stars visible at once, or in succession, in the heav- 
ens, may be regarded as one great constellation, which 
seems to revolve with a uniform motion, as if it formed one 
coherent mass ; or as if it were attached to the internal sur- 
face of a vast hollow sphere, having the earth, or rather the 
spectator, in its centre, and turning round an axis inclined 
to his horizon, so as to pass through that fixed point or pole 
already mentioned. 

(61.) Lastly, he will notice, if he have patience to out- 
watch a long winter's night, commencing at the earliest 
moment when the stars appear, and continuing till morning 
twilight, that those stars which he observed setting in the 
west have again risen in the east, while those which were 
rising when he first began to notice them have completed 
their coarse, and are now set; and that thus the hemisphere, 
or a great part of it, which was then above, is now beneath 
him, and its place supplied by that which was at first under 
his feet, which he will thus discover to be no less copiously 
furnished with stars than the other, and bespangled with 
groups no less permanent and distinctly recognizable. 
Thus he will learn that the great constellation we have 
above spoken of as revolving round the pole is coexten- 
sive with the whole surface of the sphere, being in reality 



"^OUTLINES OF ASTRONOMY 73 

nothing less than a universe of luminaries surrounding the 
earth on all sides, and brought, in succession before his 
view, and referred (each luminary according to its own 
visual ray or direction from his eye) to the imaginary 
spherical surface, of which he himself occupies the cen- 
tre. (See art. 49.) There is always, therefore (he would 
justly argue), a star-bespangled canopy over his head, by 
day as well as by night, only that the glare of daylight 
(which he perceives gradually to efface the stars as the 
morning twilight comes on) prevents them from being seen. 
And such is really the case. The stars actually continue 
visible through telescopes in the daytime; and, in propor- 
tion to the power of the instrument, not only the largest and 
brightest of them, but even those of inferior lustre, such as 
scarcely strike the eye at night as at all conspicuous, are 
readily found and followed even at noonday — unless in that 
part of the sky which is very near the sun — by those who 
possess the means of pointing a telescope accurately to the 
proper places. Indeed, from the bottoms of deep narrow 
pits, such as a well, or the shaft of a mine, such bright stars 
as pass the zenith may even be discerned by the naked eye; 
and we have ourselves heard it stated by a celebrated opti- 
cian, that the earliest circumstance which drew his attention 
to astronomy was the regular appearance, at a certain hour, 
for several successive days, of a considerable star, through 
the shaft of a chimney. Yenus in our climate, and even 
Jupiter in the clearer skies of tropical countries, are often 
visible, without any artificial aid, to the naked eye of one 
who knows nearly where to look for them. During total 
eclipses of the sun, the larger stars also appear in their 
proper situations. 

(62.) But to return to our incipient astronomer, whom 
Astronomy — Vol. XIX — 4 



74 OUTLINES OF ASTRONOMY 

we left contemplating the sphere of the heavens, as com- 
pleted in imagination beneath his feet, and as rising up 
from thence in its diurnal course. There is one portion 
or segment of this sphere of which he will not thus obtain 
a view. As there is a segment toward the north, adjacent 
to the pole above his horizon, in which the stars never set, 
so there is a corresponding segment, about which the 
smaller circles of the more southern stars are described, 
in which they never rise. The stars which border upon the 
extreme circumference of this segment just graze the south- 
ern point of his horizon, and show themselves for a few 
moments above it, precisely as those near the circumference 
of the northern segment graze his northern horizon, and dip 
for a moment below it, to reappear immediately. Every 
point in a spherical surface has, of course, another diamet- 
rically opposite to it; and as the spectator's horizon divides 
his sphere into two hemispheres — a superior and inferior — 
there must of necessity exist a depressed pole to the south, 
corresponding to the elevated one to the north, and a por- 
tion surrounding it, perpetually beneath, as there is another 
surrounding the north pole, perpetually above it. 

Hie vertex nobis semper sublimis ; at ilium 

Sub pedibus nox atra videt, manesque profundi." — Virgil 

One pole rides high, one plunged beneath the main, 
Seeks the deep night, and Pluto's dusky reign. 

(63.) To get sight of this segment, he must travel south- 
ward. In so doing, a new set of phenomena come forward. 
In proportion as he advances to the south, some of those 
constellations which, at his original station, barely grazed 
the northern horizon, will be observed to sink below it and 
set, at first remaining hid only for a very short time, but 



OUTLINES OF ASTRONOMY 75 

gradually for a longer part of the twenty-four Lours. They 
will continue, however, to circulate about the same point — 
that is, holding the same invariable position with respect to 
them in the concave of the heavens among the stars; but 
this point itself will become gradually depressed with re- 
spect to the spectator's horizon. The axis, in short, about 
which the diurnal motion is performed, will appear to have 
become continually less and less inclined to the horizon; 
and by the same degrees as the northern pole is depressed 
the southern will rise, and constellations surrounding it will 
come into view; at first momentarily, but by degrees for 
longer and longer times in each diurnal revolution — realiz- 
ing, in short, what we have already stated in art. 51. 

(6-i.) If he travel continually southward, he will at 
length reach a line on the earth's surface, called the equa- 
tor, at any point of which, indifferently, if he take up his 
station and recommence his observations, he will find that 
he has both the centres of diurnal motion in his horizon, 
occupying opposite points, the northern pole having been 
depressed, and the southern raised, so that, in this geo- 
graphical position, the diurnal rotation of the heavens will 
appear to him to be performed about a horizontal axis, 
every star describing half its diurnal circle above and half 
beneath his horizon, remaining alternately visible for twelve 
hours, and concealed during the same interval. In this situ- 
ation, no part of the heavens is concealed from his successive 
view. In a night of twelve hours (supposing such a contin- 
uance of darkness possible at the equator) the whole sphere 
will have passed in review over him — the whole hemisphere 
with which he began his night's observation will have been 
carried down beneath him, and the entire opposite one 
brought up from below. 



76 OUTLINES OF ASTRONOMY 

(65). If lie pass the equator, and travel still further 
southward, the southern pole of the heavens will become 
elevated above his horizon, and the northern will sink 
below it; and the more, the further he advances south- 
ward; and when arrived at a station as far as to the south 
of the equator as that from which he started was to the 
north, he will find the whole phenomena of the heavens 
reversed. The stars which at his original station described 
their whole diurnal circles above his horizon, and never 
set, now describe them entirely below it, and never rise, 
but remain constantly invisible to him; and vice versd, 
those stars which at his former station he never saw, he 
will now never cease to see. 

(Q6.) Finally, if, instead of advancing southward from 
his first station, he travel northward, he will observe the 
northern pole of the heavens to become more elevated 
above his horizon, and the southern more depressed below 
it. In consequence, his hemisphere will present a less 
variety of stars, because a greater proportion of the whole 
surface of the heavens remains constantly visible or con- 
stantly invisible: the circle described by each star, too, 
becomes more nearly parallel to the horizon; and, in short, 
every appearance leads to suppose that could he travel far 
enough to the north, he would at length attain a point verti- 
cally under the northern pole of the heavens, at which none 
of the stars would either rise or set, but each would circu- 
late round the horizon in circles parallel to it. Many en- 
deavors have been made to reach this point, which is called 
the north pole of the earth, but hitherto without success ; a 
barrier of almost insurmountable difficulty being presented 
by the increasing rigor of the climate : but a very near ap- 
proach to it has been made; and the phenomena of those 



OUTLINES OF ASTRONOMY 77 

regions, though not precisely such as we have described as 
what must subsist at the pole itself, have proved to be in 
exact correspondence with its near proximity. A similar 
remark applies to the south pole of the earth, which, how- 
ever, is more unapproachable, or, at least, has been less 
nearly approached, than the north. 

(67.) The above is an account of the phenomena of the 
diurnal motion of the stars, as modified by different geo- 
graphical situations, not grounded on any speculation, but 
actually observed and recorded by travellers and voyagers. 
It is, however, in complete accordance with the hypothesis 
of a rotation of the earth round a fixed axis. In order to 
show this, however, it will be necessary to premise a few 
observations on parallactic motion in general, and on the 
appearances presented by an assemblage of remote objects, 
when viewed from different parts of a small and circum- 
scribed station. 

(68.) It has been shown (art. 16) that a spectator 
in smooth motion, and surrounded by, and forming part 
of, a great system partaking of the same motion, is uncon- 
scious of his own movement, and transfers it in idea to 
objects external and unconnected, in a contrary direction; 
those which he leaves behind aj)pearing to recede from, 
and those which he advances toward to approach, him. 
Not only, however, do external objects at rest appear in 
motion generally, with respect to ourselves when we are 
in motion among them, but they appear to move one among 
the other — they shift their relative apparent places. Let any 
one travelling rapidly along a highroad fix his eye steadily 
on any object, but at the same time not entirely withdraw 
his attention from the general landscape — he will see, or 
think he sees, the whole landscape thrown into rotation. 



78 



OUTLINES OF ASTRONOMY 



and moving round that object as a centre; all objects be- 
tween it and himself appearing to move backward, or the 
contrary way to his own motion; and all beyond it, for- 
ward, or in the direction in which he moves: but let him 
withdraw his eye from that object, and fix it on another 
— a nearer one, for instance — immediately the appearance 
of rotation shifts also, and the apparent centre about which 
this illusive circulation is performed is transferred to the 
new object, which, for the moment, appears to rest. This 
apparent change of situation of objects with respect to one 
another, arising from a motion of the spectator, is called 
a parallactic motion. To see the reason of it we must con- 




sider that the position of every object is referred by us to 
the surface of an imaginary sphere of an indefinite radius, 
having our eye for its centre; and, as we advance in any 
direction, A B, carrying this imaginary sphere along with 
us, the visual rays A P, A Q, by which objects are referred 
to its surface (at o, for instance) shift their positions with 
respect to the line in which we move, A B, which serves 
as an axis or line of reference, and assume new positions, 
B P p, B Q q, revolving round their respective objects as 
centres. Their intersections, therefore, p, q, with our visual 
sphere, will appear to recede on its surface, but with differ- 
ent degrees of angular velocity in proportion to their prox- 
imity; the same distance of advance A B subtending a 



OUTLINES OF ASTRONOMY 79 

greater angle, A P B=c P p, at the near object P than 
at the remote one Q. 

(69.) A consequence of the familiar appearance we have 
adduced in illustration of these principles is worth noticing, 
as we shall have occasion to refer to it hereafter. We ob- 
serve that every object nearer to us than that on which 
our eye is fixed appears to recede, and those further from 
us to advance in relation to one another. If then we did 
not know, or could not judge by any other appearances, 
which of two objects were nearer to us, this apparent ad- 
vance or recess of one of them, when the eye is kept stead- 
ily fixed on the other, would furnish a criterion. In a dark 
night, for instance, when all intermediate objects are un- 
seen, the apparent relative movement of two lights which 
we are assured are themselves fixed, will decide as to their 
relative proximities. That which seems to advance with us 
and gain upon the other, or leave it behind it, is the 
furthest from us. 

(70.) The apparent angular motion of an object, arising, 
from a change of our point of view, is called in general 
parallax, and it is always expressed by the angle A P B 
subtended at the object P (see S.g. of art. 68) by a line join- 
ing the two points of view A B under consideration. For 
it is evident that the difference of angular position of P, 
with respect to the invariable direction A B D, when 
viewed from A and from B, is the difference of the two 
angles DBP and DAP; now, DBP being the exte- 
rior angle of the triangle A B P, is equal to the sum of 
the interior and opposite, D B P=D A P-J-A P B, whence 
DBP— D AP=APB. 

(71.) It follows from what has been said that the amount 
of parallactic motion arising from any given change of our 



W OUTLINES OF ASTRONOMY 

point of view is, cceteris paribus, less, as the distance of an 
object viewed is greater; and when that distance is ex- 
tremely great in comparison with the change in our point 
of view, the parallax becomes insensible; or, in other words, 
objects do not appear to vary in situation at all. It is on 
this principle, that in alpine regions visited for the first 
time we are surprised and confounded at the little progress 
we appear to make by a considerable change of place. An 
hour's walk, for instance, produces but a small parallactic 
change in the relative situations of the vast and distant 
masses which surround us. Whether we walk round a cir- 
cle of a hundred yards in diameter, or merely turn our- 
selves round in its centre, the distant panorama presents 
almost exactly the same aspect — we hardly seem to have 
changed our point of view. 

(72.) Whatever notion, in other respects, we may form 
of the stars, it is quite clear they must be immensely dis- 
tant. Were it not so, the apparent angular interval between 
any two of them seen overhead would be much greater than 
when seen near the horizon, and the constellations, instead 




of preserving the same appearances and dimensions during 
their whole diurnal course, would appear to enlarge as they 
rise higher in the sky, as we see a small cloud in the horizon 
swell into a great overshadowing canopy when drifted by 
the wind across our zenith, or as may be seen in the above 



OUTLINES OF ASTRONOMY 81 

figure, where a b, A B, a b, are three different positions of 
the same stars, as they would, if near the earth, be seen 
from a spectator S, under the visual angles a S b, A S B. 
No such change of apparent dimension, however, is ob- 
served. The nicest measurements of the apparent angular 
distance of any two stars inter se, taken in any parts of their 
diurnal course (after allowing for the unequal effects of re- 
fraction, or when taken at such times that this cause of dis- 
tortion shall act equally on both), manifest not the slightest 
perceptible variation. Not only this, but at whatever point 
of the earth's surface the measurement is performed, the 
results are absolutely identical. No instruments ever yet 
invented by man are delicate enough to indicate, by an 
increase or diminution of the angle subtended, that one 
point of the earth is nearer to or further from the stars 
than another. 

(73.) The necessary conclusion from this is, that the 
dimensions of the earth, large as it is, are comparatively 
nothing, absolutely imperceptible, when compared with the 
interval which separates the stars from the earth. If an 
observer walk round a circle not more than a few yards 
in diameter, and from different points in its circumference 
measure with a sextant or other more exact instrument 
adapted for the purpose, the angles P A Q, P B Q, P C Q, 
subtended at those stations by two well-defined points in 
his visible horizon, P Q, he will at once be advertised, by 
the difference of the results, of his change of distance from 
them arising from his change of place, although that differ- 
ence may be so small as to produce no change in their 
general aspect to his unassisted sight. This is one of the 
innumerable instances where accurate measurement obtained 
by instrumental means places us in a totally different situa- 



82 OUTLINES OF ASTRONOMY 

tion in respect to matters of fact, and conclusions thence 
deducible, from what we should hold, were we to rely in 
all cases on the mere judgment of the eye. To so great a 
nicety have such observations been carried by the aid of 
an instrument called a theodolite, that a circle even a few 
inches in diameter may thus be rendered sensible, may thus 
be detected to have a size, and an ascertainable place, by 
reference to objects distant by fully 100,000 times its own 
dimensions. Observations, differing, it is true, somewhat 




in method, but identical in principle, and executed with 
quite as much exactness, have been applied to the stars, 
and with a result such as has been already stated. Hence 
it follows, incontrovertibly, that the distance of the stars 
from the earth cannot be so small as 100,000 of the earth's 
diameters. It is, indeed, incomparably greater ; for we shall 
hereafter find it fully demonstrated that the distance just 
named, immense as it may appear, is yet much underrated. 
(74.) From such a distance, to a spectator with our facul- 
ties, and furnished with our instruments, the earth would be 
imperceptible; and, reciprocally, an object of the earth's 
size, placed at the distance of the stars, would be equally 
undiscernible. If, therefore, at the point on which a spec- 
tator stands, we draw a plane touching the globe, and pro- 



OUTLINES OF ASTRONOMY S3 

long it in imagination till it attain the region of the stars, 
and through the centre of the earth conceive another plane 
parallel to the former, and coextensive with it, to pass; 
these, although separated throughout their whole extent by 
the same interval, viz., a semidiameter of the earth, will 
yet, on account of the vast distance at which that interval 
is seen, be confounded together, and indistinguishable from 
each other in the region of the stars, when viewed by a 
spectator on the earth. The zone they there include will 
be of evanescent breadth to his eye, and will only mark 
out a great circle in the heavens, one and the same for 
both the stations. This great circle, when spoken of as a 
circle of the sphere, is called the celestial horizon or simply 
the horizon, and the two planes just described are also 
spoken of as the sensible and the rational horizon of the 
observer's station. 

(75.) From what has been said (art. 73) of the distance 
of the stars, it follows, that if we suppose a spectator at 
the centre of the earth to have his view bounded by the 
rational horizon, in exactly the same manner as that of a 
corresponding spectator on the surface is by his sensible 
horizon, the two observers will see the same stars in the 
same relative situations, each beholding that entire hemi- 
sphere of the heavens which is above the celestial horizon, 
corresponding to their common zenith. Now, so far as 
appearances go, it is clearly the same thing whether the 
heavens, that is, all space with its contents, revolve round 
a spectator at rest in the earth's centre, or whether that 
spectator simply turn round in the opposite direction in his 
place, and view them in succession. The aspect of the 
heavens, at every instant, as referred to his horizon (which 
must be supposed to turn with him), will be the same in 



84 OUTLINES OF ASTRONOMY 

both suppositions. And since, as has been shown, appear- 
ances are also, so far as the stars are concerned, the same to 
a spectator on the surface as to one at the centre, it follows 
that, whether we suppose the heavens to revolve without 
the earth, or the earth within the heavens, in the opposite 
direction, the diurnal phenomena, to all its inhabitants, will 
be no way different. 

(76.) The Copernican astronomy adopts the latter as the 
true explanation of these phenomena, avoiding thereby the 
necessity of otherwise resorting to the cumbrous mechanism 
of a solid but invisible sphere, to which the stars must be 
supposed attached, in order that they may be carried round 
the earth without derangement of their relative situations 
inter se. Such a contrivance would, indeed, suffice to ex- 
plain the diurnal revolution of the stars, so as to "save 
appearances"; but the movements of the sun and moon, 
as well as those of the planets, are incompatible with such 
a supposition, as will appear when we come to treat of these 
bodies. On the other hand, that a spherical mass of mod- 
erate dimensions (or, rather, when compared with the sur- 
rounding and visible universe, of evanescent magnitude), 
held by no tie, and free to move and to revolve, should do 
so, in conformity with those general laws which, so far 
as we know, regulate the motions of all material bodies, 
is so far from being a postulate difficult to be conceded, 
that the wonder would rather be should the fact prove 
otherwise. As a postulate, therefore, we shall henceforth 
regard it; and as, in the progress of our work, analogies 
offer themselves in its support from what we observe of 
other celestial bodies, we shall not fail to point them out 
to the reader's notice. 

(77.) The earth's rotation on its axis so admitted, ex- 



OUTLINES OF ASTRONOMY 85 

plaining, as it evidently does, the apparent motion of the 
stars in a completely satisfactory manner, prepares us for 
the further admission of its motion, bodily, in space, should 
such a motion enable us to explain, in a manner equally 
so, the apparently complex and enigmatical motions of the 
sun, moon, and planets. The Copernican astronomy adopts 
this idea in its full extent, ascribing to the earth, in addition 
to its motion of rotation about an axis, also one of translation 
or transference through space, in such a course or orbit, and 
so regulated in direction and celerity, as, taken in conjunc- 
tion with the motions of the other bodies of the universe, 
shall render a rational account of the appearances they suc- 
cessively present — that is to say, an account of which the 
several parts, postulates, propositions, deductions, intelli- 
gibly cohere, without contradicting each other or the 
nature of things as concluded from experience. In this 
view of the Copernican doctrine it is rather a geometrical 
conception than a physical theory, inasmuch as it simply 
assumes the requisite motions, without attempting to ex- 
plain their mechanical origin, or assign them any depen- 
dence on physical causes. The Newtonian theory of gravi- 
tation supplies this deficiency, and, by showing that all the 
motions required by the Copernican conception must, and 
that no others can, result from a single, intelligible, and 
very simple dynamical law, has given a degree of certainty 
to this conception, as a matter of fact, which attaches to no 
other creation of the human mind. 

(78.) To understand this conception in its farther de- 
velopments, the reader must bear steadily in mind the dis- 
tinction between relative and absolute motion. Nothing is 
easier to perceive than that, if a spectator at rest view 
a certain number of moving objects, they will group and 



86 OUTLINES OF ASTRONOMY 

arrange themselves to his eye, at each, successive moment, 
in a very different way from what they would do were he 
in active motion among them — if he formed one of them, 
for instance, and joined in their dance. This is evident 
from what has been said before of parallactic motion ; but 
it will be asked, How is such a spectator to disentangle 
from each other the two parts of the apparent motions of 
these external objects — that which arises from the effect 
of his own change of place, and which is therefore only 
apparent (or, as a German metaphysician would say, subjec- 
tive — having reference only to him as perceiving it)— and 
that which is real (or objective — having a positive existence, 
whether perceived by him or not) ? By what rule is he to 
ascertain, from the appearances presented to him while 
himself in motion, what would be the appearances were he 
at rest ? It by no means follows, indeed, that he would 
even then at once obtain a clear conception of all the mo- 
tions of all the objects. The appearances so presented to 
him would have still something subjective about them. 
They would be still appearances, not geometrical realities. 
They would still have a reference to the point of view, 
which might be very unfavorably situated (as, indeed, is 
the case in our system) for affording a clear notion of the 
real movement of each object. No geometrical figure, or 
curve, is seen by the eye as it is conceived by the mind 
to exist in reality. The laws of perspective interfere and 
alter the apparent directions and foreshorten the dimensions 
of its several parts. If the spectator be unfavorably situ- 
ated, as, for instance, nearly in the plane of the figure (which 
is the case we have to deal with), they may do so to such an 
extent, as to make a considerable effort of imagination nec- 
essary to pass from the sensible to the real form. 



OUTLINES OF ASTRONOMY 87 

(79.) Still, preparatory to this ultimate step, it is first 
necessary that the spectator should free or clear the ap- 
pearances from the disturbing influence of his own change 
of place. And this he can always do by the following 
general rule or proposition: 

The relative motion of two bodies is the same as if either of 
them were at rest, and all its motion communicated to the other 
in an opposite direction. 9 

Hence, if two bodies move alike, they will, when seen 
from each other (without reference to other near bodies, but 
only to the starry sphere), appear at rest. Hence, also, if 
the absolute motions of two bodies be uniform and rectilin- 
ear, their relative motion is so also. 

(80.) The stars are so distant, that as we have seen it is 
absolutely indifferent from what point of the earth's surface 
we view them. Their configurations inter se are identically 
the same. It is otherwise with the sun, moon, and planets, 
which are near enough (especially the moon) to be parol- 
lactically displaced by change of station from place to place 
on our globe. In order that astronomers residing on differ- 
ent points of the earth's surface should be able to compare 
their observations with effect, it is necessary that they 
should clearly understand and take account of this effect 
of the difference of their stations on the appearance of the 
outward universe as seen from each. As an exterior object 
seen from one would appear to have shifted its place were 



9 This proposition is equivalent to the following, which precisely meets the 
case proposed, but requires somewhat more thought for its clear apprehension 
than can perhaps be expected from a beginner : 

Prop. — If two todies, A and B, be in motion independently of each other, the 
motion which B seen from A would appear to have if A were at rest is the same 
with that which it would appear to have, A being in motion, if, in addition to its 
own motion, a motion equal to A's and in the same direction w&re communi- 
cated to it. 



88 OUTLINES OF ASTRONOMY 

the spectator suddenly transported to the other, so two 
spectators, viewing it from the two stations at the same 
instant, do not see it in the same direction. Hence arises 
a necessity for the adoption of a conventional centre of ref 
erence, or imaginary station of observation common to all 
the world, to which each observer, wherever situated, may 
refer (or, as it is called, reduce) his observations, by calcu- 
lating and allowing for the effect of his local position with 
respect to that common centre (supposing him to possess 
the necessary data). If there were only two observers, in 




fixed stations, one might agree to refer his observations to 
the other station; but, as every locality on the globe may 
be a station of observation, it is far more convenient and 
natural to ftx. upon a point equally related to all, as the 
common point of reference; and this can be no other than 
the centre of the globe itself. The parallactic change of 
apparent place which would arise in an object, could any 
observer suddenly transport himself to the centre of the 
earth, is evidently the angle C S P, subtended at the ob- 
ject S by that radius C P of the earth which joins its cen- 
tre and the place P of observation. 



OUTLINES OF ASTRONOMY 89 



CHAPTER II 



Terminology and Elementary Geometrical Conceptions and Relations — Ter- 
minology relating to the Globe of the Earth — To the 
Celestial Sphere — Celestial Perspective 



(81.) Several of the terms in use among astronomers 
have been explained in the preceding chapter, and others 
nsed anticipatively. But the technical language of every 
subject requires to be formally stated, both for consistency 
of usage and definiteness of conception. We shall there- 
fore proceed, in the first place, to define a number of terms 
in perpetual use, having relation to the globe of the earth 
and the celestial sphere. 

(82.) Definition 1. The axis of the earth is that diame- 
ter about which it revolves, with a uniform motion, from 
west to east; performing one revolution in the interval which 
elapses between any star leaving a certain point in the heav- 
ens, and returning to the same point again. 

(83.) Def. 2. The poles of the earth are the points 
where its axis meets its surface. The North Pole is that 
nearest to Europe; the South Pole that most remote 
from it. 

(84.) Def. 3. The earth's equator is a great circle on 
its surface, equidistant from its poles, dividing it into two 
hemispheres — a northern and a southern; in the midst of 
which are situated the respective poles of the earth of those 
names. The plane of the equator is, therefore, a plane 
perpendicular to the earth's axis, and passing through 
its centre. 



90 OUTLINES OF ASTRONOMY 

(85.) Def. 4. The terrestrial meridian of a station on 
the earth's surface, is a great circle of the globe passing 
through both poles and through the place. The plane of 
the meridian is the plane in which that circle lies. 

(86.) Def. 5. The sensible and the rational horizon of 
any station have been already denned in art. 74. 

(87.) Def. 6. A meridian line is the line of intersection 
of the plane of the meridian of any station with the plane 
of the sensible horizon, and therefore marks the north and 
south points of the horizon, or the directions in which a 
spectator must set out if he would travel directly toward 
the north or south pole. 

(88.) Def. 7. The latitude of a place on the earth's sur- 
face is its angular distance from the equator, measured on 
its own terrestrial meridian: it is reckoned in degrees, min- 
utes, and seconds, from up to 90°, and northward or south- 
ward, according to the hemisphere the place lies in. Thus, 
the observatory at Greenwich is situated in 51° 28' 40" north 
latitude. This definition of latitude, it will be observed, is 
to be considered as only temporary. A more exact knowl- 
edge of the physical structure and figure of the earth, and 
a better acquaintance with the niceties of astronomy, will 
render some modification of its terms, or a different man- 
ner of considering it, necessary. 

(89.) Def. 8. Parallels of latitude are small circles on the 
earth's surface parallel to the equator. Every point in such 
a circle has the same latitude. Thus, Greenwich is said to 
be situated in the parallel of 51° 28' 40". 

(90.) Def. 9. The longitude of a place on the earth's sur- 
face is the inclination of its meridian to that of some fixed 
station referred to as a point to reckon from. English as- 
tronomers and geographers use the observatory at Green- 



OUTLINES OF ASTRONOMY 91 

wich for this station; foreigners, the principal observatories 
of their respective nations. Some geographers have adopted 
the island of Ferro. Hereafter, when we speak of longi- 
tude, we reckon from Greenwich. The longitude of a place 
is, therefore, measured by the arc of the equator intercepted 
between the meridian of the place and that of Greenwich ; 
or, which is the same thing, by the spherical angle at the 
pole included between these meridians. 

(91.) As latitude is reckoned north or south, so longi- 
tude is usually said to be reckoned west or east. It would 
add greatly, however, to systematic regularity, and tend 
much to avoid confusion and ambiguity in computations, 
were this mode of expression abandoned, and longitudes 
reckoned invariably westward from their origin round the 
whole circle from to 360°. Thus, the longitude of Paris 
is, in common parlance, either 2° 20' 22' east, or 357° 39' 38" 
west of Greenwich. But, in the sense in which we shall 
henceforth use and recommend others to use the term, the 
latter is its proper designation. Longitude is also reckoned 
in time at the rate of 24h. for 360°, or 15° per hour. In this 
system the longitude of Paris is 23h. 50m. 39 Js. ' 

(92.) Knowing the longitude and latitude of a place, it 
may be laid down on an artificial globe; and thus a map of 
the earth may be constructed. Maps of particular countries 
are detached portions of this general map, extended into 
planes; or, rather, they are representations on planes of such 
portions, executed according to certain conventional systems 
of rules, called projections, the object of which is either to 



1 To distinguish minutes and seconds of time from those of angular measure 
we shall invariably adhere to the distinct system of notation here adopted (° ' ", 
and h. m. s.). Great confusion sometimes arises from the practice of using the 
same marks for both. 



92 OUTLINES OF ASTRONOMY 

distort as little as possible the outlines of countries from 
what they are on the globe — or to establish easy means of 
ascertaining, by inspection or graphical measurement, the 
latitudes and longitudes of places which occur in them, 
without referring to the globe or to books — or for other 
peculiar uses. See Chap. IY. 

(93.) Def. 10. The Tropics are two parallels of latitude, 
one on the north and the other on the south side of the 
equator, over every point of which, respectively, the sun 
in its diurnal course passes vertically on the 21st of June 
and the 21st of December in every year. Their latitudes 
are about 23° 28' respectively, north and south. 

(94.) Def. 11. The Arctic and Antarctic circles are two 
small circles or paralleis of latitude as distant from the 
north and south poles as the tropics are from the equator, 
that is to say, about 23° 28'; their latitudes, therefore, are 
about 66° 32'. We say about, for the places of these circles 
and of the tropics are continually shifting on the earth's 
surface, though with extreme slowness, as will be ex- 
plained in its proper place. 

(95.) Def. 12. The sphere of the heavens or of the stars 
is an imaginary spherical surface of infinite radius, having 
the eye of any spectator for its centre, and which may be 
conceived as a ground on which the stars, planets, etc., the 
visible contents of the universe, are seen projected as in a 
vast picture. 3 



2 The ideal sphere without us, to which we refer the places of objects, and 
which we carry along with us wherever we go, is no doubt intimately connected 
by association with, if not entirely dependent on that obscure perception of sen- 
sation in the retinae of our eyes, of which, even when closed and unexcited, we 
cannot entirely divest them. We have a real spherical surface within our eyes, 
the seat of sensation and vision, corresponding, point for point, to the external 
sphere. On this the stars, etc., are really mapped down, as we have supposed 
them in the text to be, on the imaginary concave of the heavens. When the 



OUTLINES OF ASTRONOMY 93 

(96.) Def. 13. The poles of the celestial sphere are the 
points of that imaginary sphere toward which the earth's 
axis is directed. 

(97.) Def. 14. The celestial equator, or, as it is often 
called by astronomers, the equinoctial, is a great circle of 
the celestial sphere, marked out by the indefinite extension 
of the plane of the terrestrial equator. 

(98.) Def. 15. The celestial horizon of any place is a 
great circle of the sphere marked out by the indefinite ex- 
tension of the plane of any spectator's sensible or (which 
comes to the same thing, as will presently be shown), his 
rational horizon, as in the case of the equator. 

(99.) Def. 16. The zenith and nadir 3 of a spectator are 
the two points of the sphere of the heavens, vertically over 
his head, and vertically under his feet, or the poles of the 
celestial horizon; that is to say, points 90° distant from 
every point in it. 

(100.) Def. 17. Vertical circles of the sphere are great 
circles passing through the zenith and nadir, or great cir- 
cles perpendicular to the horizon. On these are measured 
the altitudes of objects above the horizon — the complements 
to which are their zenith distances. 

(101.) Def. 18. The celestial meridian of a spectator is 
the great circle marked out on the sphere by the prolonga- 
tion of the plane of his terrestrial meridian. If the earth 



whole surface of the retina is excited by light, habit leads us to associate it 
with the idea of a real surface existing without us. Thus we become impressed 
with the notion of a sky and a heaven, but the concave surface of the retina 
itself is the true seat of all visible angular dimension and angular motion. The 
substitution of the retina for the heavens would be awkward and inconvenient 
in language, but it may always be mentally made. (See Schiller's pretty enigma 
on the eye in his Turandot.) 

3 From Arabic words, semt, vertex, and almadhir, corresponding or opposite 
to ; nadir corresponds evidently to the German nieder (down), whence our nether. 



94 OUTLINES OF ASTRONOMY 

be supposed at rest, this is a fixed circle, and all the stars 
are carried across it in their diurnal courses from east to 
west. If the stars rest and the earth rotate, the spectator's 
meridian, like his horizon (art. 52), sweeps daily across the 
stars from west to east. Whenever in future we speak of 
the meridian of a spectator or observer, we intend the 
celestial meridian, which being a circle passing through 
the poles of the heavens and the zenith of the observer, 
is necessarily a vertical circle, and passes through the 
north and south points of the horizon. 

(102.) Def. 19. The prime vertical is a vertical circle 
perpendicular to the meridian, and which therefore passes 
through the east and west points of the horizon. 

(103.) Def. 20. Azimuth is the angular distance of a 
celestial object from the north or south point of the hori- 
zon (according as it is the north or south pole which is 
elevated), when the object is referred to the horizon by a 
vertical circle; or it is the angle comprised between two 
vertical planes — one passing through the elevated pole, the 
other through the object. Azimuth may be reckoned east- 
ward or westward, from the north or south point, and is 
usually so reckoned only to 180° either way. But to avoid 
confusion, and to preserve continuity of interpretation when 
algebraic symbols are used (a point of essential importance, 
hitherto too little insisted on), we shall always reckon azi- 
muth from the point of the horizon most remote from the 
elevated pole, westward (so as to agree in general directions 
with the apparent diurnal motion of the stars), and carry 
its reckoning from 0° to 360° if always reckoned positive, 
considering the eastward reckoning as negative. 

(104.) Def. 21. The altitude of a heavenly body is its 
apparent angular elevation above the horizon. It is the 



OUTLINES OF ASTRONOMY 95 

complement to 90°, therefore, of its zenith distance. The 
altitude and azimuth of an object being known, its place 
in the visible heavens is determined. 

(105.) Def. 22. The declination of a heavenly body is its 
angular distance from the equinoctial or celestial equator, 
or the complement to 90° of its angular distance from the 
nearest pole, which latter distance is called its Polar dis- 
tance. Declinations are reckoned plus or minus, according 
as the object is situated in the northern or southern celestial 
hemisphere. Polar distances are always reckoned from the 
North Pole, from 0° up to 180°, by which all doubt or 
ambiguity of expression with respect to sign is avoided. 

(106.) Def. 23. Hour circles of the sphere, or circles 
of declination, are great circles passing through the poles, 
and of course perpendicular to the equinoctial. The hour 
circle, passing through any particular heavenly body, serves 
to refer it to a point in the equinoctial, as a vertical circle 
does to a point in the horizon. 

(107.) Def. 24. The hour angle of a heavenly body is 
the angle at the pole included between the hour circle pass- 
ing through the body, and the celestial meridian of the 
place of observation. We shall always reckon it positively 
from the upper culmination (art. 125) westward, or in con- 
formity with the apparent diurnal motion, completely round 
the circle from 0° to 360°. Hour angles, generally, are 
angles included at the pole between different hour circles. 

(108.) Def. 25. The right ascension of a heavenly body 
is the arc of the equinoctial included between a certain 
point in that circle called the Vernal Equinox, and the 
point in the same circle to which it is referred by the cir- 
cle of declination passing through it. Or it is the angle 
included between two hour circles, one of which passes 



96 OUTLINES' OF ASTRONOMY 

through the vernal equinox (and is called the equinoctial 
colure), the other through the body. How the place of this 
initial point on the equinoctial is determined, will be ex- 
plained further on. 

(109.) The right ascensions of celestial objects are 
always reckoned eastward from the equinox, and are es- 
timated either in degrees, minutes and seconds, as in the 
case of terrestrial longitudes, from 0° to 360°, which com- 
pletes the circle; or, in time, in hours, minutes and sec- 
onds, from Oh. to 24h. The apparent diurnal motion of 
the heavens being contrary to the real motion of the earth, 
this is in conformity with the westward reckoning of longi- 
tudes. (Art. 91.) 

(110.) /Sidereal time is reckoned by the diurnal motion 
of the stars, or rather of that point in the equinoctial from 
which right ascensions are reckoned. This point may be 
considered as a star, though no star is, in fact, there ; and, 
moreover, the point itself is liable to a certain slow varia- 
tion — so slow, however, as not to affect, perceptibly, the in- 
terval, of any two of its successive returns to the meridian. 
This interval is called a sidereal day, and is divided into 
24 sidereal hours, and these again into minutes and sec- 
onds. A clock which marks sidereal time, i.e. which goes 
at such a rate as always to show Oh. 0m. 0s. when the equi- 
nox comes on the meridian, is called a sidereal clock, and 
is an indispensable piece of furniture in every observatory. 
Hence the hour angle of an object reduced to time at the 
rate of 15° per hour, expresses the interval of sidereal time 
by which (if its reckoning be positive) it has passed the me- 
ridian; or if negative, the time it wants of arriving at the 
meridian of the place of observation. So also the right 
ascension of an object, if converted into time at the same 



OUTLINES OF ASTRONOMY 97 

rate (since 360° being described uniformly in 24 hours, 
15° must be so described in 1 hour), will express the inter- 
val of sidereal time which, elapses from the passage of the 
vernal equinox across the meridian to that of the object 
next subsequent. 

(111.) As a globe or maps may be made of the whole 
or particular regions of the surface of the earth, so also a 
globe, or general map of the heavens, as well as charts of 
particular parts, may be constructed, and the stars laid 
down in their proper situations relative to each other, and 
to the poles of the heavens and the celestial equator. Such 
a representation, once made, will exhibit a true appearance 
of the stars as they present themselves in succession to 
every spectator on the surface, or as they may be con- 
ceived to be seen at once by one at the centre of the 
globe. It is, therefore, independent of all geographical 
localities. There will occur in such a representation nei- 
ther zenith, nadir, nor horizon — neither east nor west 
points; and although great circles may be drawn on it 
from pole to pole, corresponding to terrestrial meridians, 
they can no longer, in this point of view, be regarded as 
the celestial meridians of fixed points on the earth's surface, 
since, in the course of one diurnal revolution, every point 
in it passes beneath each of them. It is on account of this 
change of conception, and with a view to establish a com- 
plete distinction between the two branches of Geography 
and Uranography,* that astronomers have adopted different 
terms (viz., declination and right ascension) to represent 
those arcs in the heavens which correspond to latitudes 
and longitudes on the earth. It is for this reason that 
they term the equator of the heavens the equinoctial ; that 

4 Ttj, the earth ; ypa^eiv, to describe or represent ; ovpavo?, the heaven. 
Astronomy— Vol. XIX.— 5 



98 



OUTLINES OF ASTRONOMY 



what are meridians on the earth are called hour circles in 
the heavens, and the angles they include between them 
at the poles are called hour angles. All this is convenient 
and intelligible; and had they been content with this no- 
menclature, no confusion could ever have arisen. Unluck- 
ily, the early astronomers have employed also the words 
latitude and longitude in their uranography, in speaking 
of arcs of circles not corresponding to those meant by the 
same words on the earth, but having reference to the mo- 
tion of the sun and planets among the stars. It is now too 
late to remedy this confusion, which is ingrafted into every 
existing work on astronomy: we can only regret, and warn 
the reader of it, that he may be on his guard when, at a 
more advanced period of our work, we shall have occasion 
to define and use the terms in their celestial sense, at the same 
time urgently recommending to future writers the adoption 
of others in their places. 

(112.) It remains to illustrate these descriptions by refer- 
ence to a figure. Let C be the centre of the earth, N C S its 



/ / A/ / / dx \ 



axis; then are N and S its ^oZes; E Q its equator \ A B the 
parallel of latitude of the station A on its surface; A P par- 



OUTLINES OF ASTR0X02IY 



99 



allel to S C N, the direction in which an observer at A will 
see the elevated pole of the heavens; and A Z, the prolon- 
gation of the terrestrial radius C A, that of his zenith. 
N A E S will be his meridian; N G S that of some fixed 
station, as Greenwich; and G E, or the spherical angle 
GNE, his longitude, and E A his latitude. Moreover, if 
n s be a plane touching the surface in A, this will be his 
sensible horizon; n A s marked on that plane bj its inter- 
section with his meridian will be his meridian line, and 
n and s the north and south points of his horizon. 

(113.) Again, neglecting the size of the earth, or con- 
ceiving him stationed at its centre, and referring every- 
thing to his rational horizon; let the annexed figure rep- 
resent the sphere of the heavens; C the spectator; Z his 
zenith; and N his nadir: then will H A O, a great circle 
of the sphere, whose poles are Z N, be his celestial hori- 




zon; P p the elevated and depressed POLES of the heavens; 
H P the altitude of the pole, and H P Z E O his merid- 
ian; E T Q, a great circle perpendicular to P p, will be 
the equinoctial; and if Y represent the equinox, Y T will 
be the right ascension, T S the declination, and P S the 
polar distance of any star or object S, referred to the equi- 



100 OUTLINES OF ASTRONOMY 

noctial by the hour circle P S T p; and BSD will be 
the diurnal circle it will appear to describe about the pole. 
Again, if we refer it to the horizon by the vertical circle 
Z S M, O M will be its azimuth, M S its altitude, and Z S 
its zenith distance. H and are the north and south, e w 
the east and west points of his horizon, or of the heavens. 
Moreover, if H A, O o, be small circles, or parallels of decli- 
nation, touching the horizon in its north and south points, 
H h will be the circle of perpetual apparition, between 
which and the elevated pole the stars never set; O o that 
of perpetual occultation, between which and the depressed 
pole they never rise. In all the zone of the heavens be- 
tween H h and O o, they rise and set; any one of them, 
as S, remaining above the horizon in that part of its diurnal 
circle represented by a B A, and below it throughout all 
the part represented by A D a. It will exercise the reader 
to construct this figure for several different elevations of the 
pole, and for a variety of positions of the star S in each. 

(114.) Celestial perspective is that branch of the general 
science of perspective which teaches us to conclude, from 
a knowledge of the real situation and forms of objects, 
lines, angles, motions, etc., with respect to the spectator, 
their apparent aspects, as seen by him projected on the 
imaginary concave of the heavens; and, vice versd, from 
the apparent configurations and movements of objects so 
seen projected, to conclude, so far as they can be thence 
concluded, their real geometrical relations to each other 
and to the spectator. It agrees with ordinary perspective 
when only a small visual area is contemplated, because the 
concave ground of the celestial sphere, for a small extent, 
may be regarded as a plane surface, on which objects are 
seen projected or depicted as in common perspective. But 



OUTLINES OF ASTRONOMY 101 

when large amplitudes of the visual area are considered, or 
when the whole contents of space are regarded as projected 
en the whole interior surface of the sphere, it becomes 
necessary to use a different phraseology, and to resort to 
a different form of conception. In common perspective 
there is a single "point of sight," or "centre of the pic- 
ture," the visual line from the eye to which is perpen- 
dicular to the "plane of the picture," and all straight lines 
are represented by straight lines. In celestial perspective, 
every point to which the view is for the moment directed, 
is equally entitled to be considered as the "centre of the 
picture, ' ' every portion of the surface of the sphere being 
similarly related to the eye. Moreover, every straight line 
(supposed to be indefinitely prolonged) is projected into 
a semicircle of the sphere, that, namely, in which a plane 
passing through the line and the eye cuts its surface. And 
every system of parallel straight lines, in whatever direc- 
tion, is projected into a system of semicircles of the sphere, 
meeting in two common apexes, or vanishing points, dia- 
metrically opposite to each other, one of which corresponds 
to the vanishing point of parallels in ordinary perspective ; 
the other in such perspective has no existence. In other 
words, every point in the sphere to which the eye is directed 
may be regarded as one of the vanishing points, or one 
apex of a system of straight lines parallel to that radius 
of the sphere which passes through it or to the direction 
of the line of sight, seen in perspective from the earth, 
and the point diametrically opposite, or that from which 
he is looking, as the other. And any great circle of the 
sphere may similarly be regarded as the vanishing circle of 
a system of planes, parallel to its own. 

(115.) A familiar illustration of this is often to be had 



102 OUTLINES OF ASTRONOMY 

by attending to the lines of light seen in the air, when 
the sun's rays are darted through apertures in clouds, 
the sun itself being at the time obscured behind them 
These lines which, marking the course of rays emanating 
from a point almost infinitely distant, are to be considered 
as parallel straight lines, are thrown into great circles of 
the sphere, having two apexes or points of common inter- 
section — one in the place where the sun itself (if not ob- 
scured) would be seen, the other diametrically opposite. 
The first only is most commonly suggested when the spec- 
tator's view is toward the sun. But in mountainous coun- 
tries, the phenomenon of sunbeams converging toward 
a point diametrically opposite to the sun, and as much 
depressed below the horizon as the sun is elevated above 
it, is not infrequently noticed, the back of the spectator 
being turned to the sun's place. Occasionally, but much 
more rarely, the whole course of such a system of sun- 
beams, stretching in semicircles across the hemisphere 
from horizon to horizon (the sun being near setting), may 
be seen. * Thus again, the streamers of the Aurora Borealis, 
which are doubtless electrical rays, parallel, or nearly paral- 
lel to each other, and to the dipping-needle, usually appear 
to diverge from the point toward which the needle, freely 
suspended, would dip northward (i.e. about 70° below the 

6 It is in such cases only that we conceive them as circles, the ordinary 
conventions of plane perspective becoming untenable. The author had the good 
fortune to witness on one occasion the phenomenon described in the text under 
circumstances of more than usual grandeur. Approaching Lyons from the south 
on September 30, 1826, about "5£ h. P.M., the sun was seen nearly setting be- 
hind broken masses of stormy cloud, from whose apertures streamed forth 
beams of rose- colored light, traceable all across the hemisphere almost to their 
opposite point of convergence behind the snowy precipices of Mont Blanc, con- 
spicuously visible at nearly 100 miles to the eastward. The impression pro- 
duced was that of another but feebler sun about to rise from behind the 
mountain, and darting forth precursory beams to meet those of the real on© 
opposite. 



OUTLINES OF ASTRONOMY 103 

horizon and 23° west of north from London), and in their 
upward progress pursue the course of great circles till they 
again converge (in appearance) toward the point diametri- 
cally opposite {i.e. 70° above the horizon and 23° to the 
eastward of south), forming a sort of canopy overhead, 
having that point for its centre. So also in the phenom- 
enon of shooting stars, the lines of direction which they 
appear to take on certain remarkable occasions of periodical 
recurrence, are observed, if prolonged backward, apparently 
to meet nearly in one point of the sphere; a certain indica- 
tion of a general near approach to parallelism in the real 
directions of their motions on those occasions. On which 
subject more hereafter. 

(116.) In relation to this idea of celestial perspective, 
we may conceive the north and south poles of the sphere 
as the two vanishing points of a system of lines parallel to 
the axis of the earth; and the zenith and nadir of those 
of a system of perpendiculars to its surface at the place of 
observation, etc. It will be shown that the direction of a 
plumb-line at every place is perpendicular to the surface 
of still water at that place, which is the true horizon ; and 
though mathematically speaking no two plumb-lines are 
exactly parallel (since they converge to the earth's centre), 
yet over very small tracts, such as the area of a building 
— in one and the same town, etc., the difference from 
exact parallelism is so small that it may be practically 
disregarded. fl To a spectator looking upward such a system 
of plumb-lines will appear to converge to his zenith; down- 
ward, to his nadir. 



6 An interval of a mile corresponds to a convergence of plumb-lines amount- 
ing to somewhat less space than a minute. 



104 OUTLINES OF ASTRONOMY 

(117.) So, also the celestial equator, or the equinoctial, 
must be conceived as the vanishing circle of a system of 
planes parallel to the earth's equator, or perpendicular to 
its axis. The celestial horizon of any spectator is in like 
manner the vanishing circle of all planes parallel to his 
true horizon, of which planes his rational horizon (passing 
through the earth's centre) is one, and his sensible horizon 
(the tangent plane of his station) another. 

(118.) Owing, however, to the absence of all the ordinary 
indications of distance which influence our judgment in re- 
spect of terrestrial objects ; owing to the want of determinate 
figure and magnitude in the stars and planets as commonly 
seen — the projection of the celestial bodies on the ground 
of the heavenly concave is not usually regarded in this its 
true light of a perspective representation or picture, and it 
even requires an effort of imagination to conceive them 
in their true relations, as at vastly different distances, one 
behind the other, and forming with one another lines of 
junction violently foreshortened, and including angles alto- 
gether differing from those which their projected represen- 
tations appear to make. To do so at all with effect presup- 
poses a knowledge of their actual situations in space, which 
it is the business of astronomy to arrive at by appropriate 
considerations. But the connections which subsist among 
the several parts of the picture, the purely geometrical rela- 
tions among the angles and sides of the spherical triangles 
of which it consists, constitute, under the name of Uranom- 
etry, v a preliminary and subordinate branch of the general 
science, with which it is necessary to be familiar before any 
further progress can be made. Some of the most elementary 

' Oupavos, the heavens ; neroeiv, to measure ; the measurement of the heavens. 



OUTLINES OF ASTRONOMY 105 

and frequently occurring of these relations we proceed to 
explain. And first, as immediate consequences of the above 
definitions, the following propositions will be borne in mind. 

(119.) The altitude of the elevated pole is equal to the lati- 
tude of the spectator's geographical station. 

For it appears, see fig. art. 112, that the angle PAZ 
between the pole and the zenith is equal to 1ST C A, and 
the angles Z A n and N C E being right angles, we have 
P A n= A C E. Now the former of these is the elevation 
of the pole as seen from E, the latter is the angle at the 
earth's centre subtended by the arc E A, or the latitude 
of the place. 

(120.) Hence to a spectator at the north pole of the 
earth, the north pole of the heavens is in his zenith. As 
he travels southward it becomes less and less elevated till 
he reaches the equator, when both poles are in his horizon 
— south of the equator the north pole becomes depressed be- 
low, while the south rises above his horizon, and continues 
to do so till the south pole of the globe is reached, when 
that of the heavens will be in the zenith. 

(121.) The same stars, in their diurnal revolution, come 
to the meridian, successively ', of every place on the globe 
once in twenty- four sidereal hours. And, since the diurnal 
rotation is uniform, the interval, in sidereal time, which 
elapses between the same star coming upon the meridians 
of two different places is measured by the difference of 
longitudes of the places. 

(122.) Vice versa — the interval elapsing between two 
different stars coming on the meridian of one and the same 
place, expressed in sidereal time, is the measure of the 
difference of right ascensions of the stars. 

(123.) The equinoctial intersects the horizon in the east 



106 OUTLINES OF ASTRONOMY ' 

and west points, and the meridian in a point whose altitude 
is equal to the co-latitude of the place. Thus, at Green- 
wich, of which the latitude is 51° 28' 40", the altitude of 
the intersection of the equinoctial and meridian is 38° 31' 
20". The north and south poles of the heavens are the 
poles of the equinoctial. The east and west points of the 
horizon of a spectator are the poles of his celestial merid- 
ian. The north and south points of his horizon are the 
poles of his prime vertical, and his zenith and nadir are 
the poles of his horizon. 

(124.) All the heavenly bodies culminate (i.e. come to 
their greatest altitudes) on the meridian; which is, there- 
fore, the best situation to observe them, being least con- 
fused by the inequalities and vapors of the atmosphere, as 
well as least displaced by refraction. 

(125.) All celestial objects within the circle of perpetual 
apparition come twice on the meridian, above the horizon, 
in every diurnal revolution; once above and once below the 
pole. These are called their upper and lower culminations. 

(126.) The problems of uranometry, as we have described 
it, consist in the solution of a variety of spherical triangles, 
both right and oblique angled, according to the rules, and 
by the formulae of spherical trigonometry, which we suppose 
known to the reader, or for which he wij.ll consult appro- 
priate treatises. We shall only here observe generally, that 
in all problems in which spherical geometry is concerned, 
the student will find it a useful practical maxim rather to 
consider the poles of the great circles which the question 
before him refers to than the circles themselves. To use, 
for example, in the relations he has to consider, polar dis- 
tances rather than declinations, zenith distances rather than 
altitudes, etc. Bearing this in mind, there are few prob- 



OUTLINES OF ASTRONOMY 107 

lems in uranometry which will offer any difficulty. The 
following are the combinations which most commonly 
occur for solution when the place of one celestial object only 
on the sphere is concerned. 

(127.) In the triangle Z P S, Z is the zenith, P the ele- 
vated pole, and S the star, sun, or other celestial object. 
In this triangle occur, 1st, P Z, which being the comple- 
ment of P H (the altitude of the pole), is obviously the 
complement of the latitude (or the co-latitude, as it is called) 
of the place; 2d, P S, the polar distance, or the complement 
of the declination (co- declination) of the star; 3d, Z S, the 
zenith distance or co- altitude of the star. If P S be greater 
than 90°, the object is situated on the side of the equinoctial 
opposite to that of the elevated pole. If Z S be so, the 
object is below the horizon. 

In the same triangle the angles are, 1st, Z P S the hour 
angle; 2d, P Z S (the supplement of S Z 0, which latter is 
the azimuth of the star or other heavenly body) ; 3d, P S Z, 
an angle which, from the infrequency of any practical refer- 
ence to it, has not acquired a name. 8 

The following five astronomical magnitudes, then, occur 
among the sides and angles of this most useful triangle: 
viz., 1st, the co-latitude of the place of observation; 2d, 
the polar distance; 3d, the zenith distance; 4th, the hour 
angle; and 5th, the sub- azimuth (supplement of azimuth) 
of a given celestial object; and by its solution therefore 
may all problems be resolved, in which three of these 
magnitudes are directly or indirectly given, and the other 
two required to be found. 

8 In the practical discussion of the measures of double stars and other 
objects by the aid of the position micrometer, this angle is sometimes required 
to be known ; and, when so required, it will be not inconveniently referred to as 
"the angle of position of the zenith." 



108 



OUTLINES OF ASTRONOMY 



(128.) For example, suppose the time of rising or setting 
of the sun or of a star were required, having given its right 
ascension and polar distance. The star rises when appar- 
ently on the horizon, or really about 34' below it (owing to 
refraction), so that, at the moment of its apparent rising, 
its zenith distance is 90° 34' =Z S. Its polar distance P S 



B 


z 
/ /v\\ 


Is^r* f /^iC\ 


T7^\ 


y^iij, 


^r-f 


D \ / / 


/ jp 
is 



being also given, and the co- latitude Z P of the place, we 
have given the three sides of the triangle, to find the hour 
angle Z P S, which, being known, is to be added to or sub- 
tracted from the star's right ascension, to give the sidereal 
time of setting or rising, which, if we please, may be con- 
verted into solar time by the proper rules and tables. 

(129.) As another example of the use of the same trian- 
gle, we may propose to find the local sidereal time, and the 
latitude of the place of observation, by observing equal 
altitudes of the same star east and west of the meridian, and 
noting the interval of the observations in sidereal time. 

The hour angles corresponding to equal altitudes of a 
fixed star being equal, the hour angle east or west will be 
measured by half the observed interval of the observations. 
In our triangle, then, we have given this hour angle Z P S, 
the polar distance P S of the star, and Z S, its co- altitude at 



OUTLINES OF ASTRONOMY 109 

the moment of observation. Hence we may find P Z, the 
co- latitude of the place. Moreover, the hour angle of the 
star being known, and also its right ascension, the point of 
the equinoctial is known, which is on the meridian at the 
moment of observation; and, therefore, the local sidereal 
time at that moment. This is a very useful observation for 
determining the latitude and time at an unknown station. 



CHAPTEK III" 

Of the Nature of Astronomical Instruments and Observations in General 
— Of Sidereal and Solar Time — Of the Measurements of Time — 
Clocks, Chronometers — Of Astronomical Measurements — Principle of 
Telescopic Sights to Increase the Accuracy of Pointing — Simplest 
Application of this Principle — The Transit Instrument — Of the Meas- 
urement of Angular Intervals — Methods of Increasing the Accuracy of 
Reading — The Vernier — The Microscope — Of the Mural Circle — The 
Meridian Circle — Fixation of Polar and Horizontal Points — The Level, 
Plumb-line, Artificial Horizon — Principle of Collimation — Collimators 
of Rittenhouse, Kater and Bohnenberger — Of Compound Instruments 
with Co-ordinate Circles — The Equatorial, Altitude and Azimuth In- 
strument — Theodolite — Of the Sextant and Reflecting Circle — Principle 
of Repetition — Of Micrometers — Parallel Wire Micrometer — Principle 
of the Duplication of Images — The Heliometer — Double Refracting 
Eye-piece — Variable Prism Micrometer — Of the Position Micrometer 
— Illumination of Wires — Solar Telescope and Eye-piece — Helioscopy 
— Collimation of large Reflectors 

(130.) Our first chapters have been devoted to the ac- 
quisition chiefly of preliminary notions respecting the globe 
we inhabit, its relation to the celestial objects which sur- 
round it, and the physical circumstances under which all 

1 The student who is anxious to become acquainted with the chief subject 
matter of this work, may defer the reading of that part of this chapter which 
is devoted to the description of particular instruments, or content himself with 
a cursory perusal of it, until further advanced, when it will be necessary to 
return to it. 



110 OUTLINES OF ASTRONOMY 

astronomical observations must be made, as well as to pro- 
vide ourselves with a stock of technical words and elemen- 
tary ideas of most frequent and familiar use in the sequel. 
We might now proceed to a more exact and detailed state- 
ment of the facts and theories of astronomy; but, in order 
to do this with full effect, it will be desirable that the reader 
be made acquainted with the principal means which astrono- 
mers possess, of determining, with the degree of nicety their 
theories require, the data on which they ground their con- 
clusions; in other words, of ascertaining by measurement 
the apparent and real magnitudes with which they are con- 
versant. It is only when in possession of this knowledge 
that he can fully appreciate either the truth of the theories 
themselves, or the degree of reliance to be placed on any of 
their conclusions antecedent to trial: since it is only by 
knowing what amount of error can certainly be perceived 
and distinctly measured, that he can satisfy himself whether 
any theory offers so close an approximation, in its numer- 
ical results, to actual phenomena, as will justify him in re- 
ceiving it as a true representation of nature. 

(131.) Astronomical instrument- making may be justly 
regarded as the most refined of the mechanical arts, and 
that in which the nearest approach to geometrical precision 
is required, and has been attained. It may be thought an 
easy thing, by one unacquainted with the niceties required, 
to turn a circle in metal, to divide its circumference into 360 
equal parts, and these again into smaller subdivisions — to 
place it accurately on its centre, and to adjust it in a given 
position; but practically it is found to be one of the most 
difficult. Nor will this appear extraordinary, when it is 
considered that, owing to the application of telescopes to 
the purposes of angular measurement, every imperfection 



OUTLINES OF ASTRONOMY 111 

of structure or division becomes magnified by the whole 
optical power of that instrument; and that thus, not only 
direct errors of workmanship, arising from unsteadiness of 
hand or imperfection of tools, but those inaccuracies which 
originate in far more uncontrollable causes, such as the 
unequal expansion and contraction of metallic masses by a 
change of temperature, and their unavoidable flexure or 
bending by their own weight, become perceptible and 
measurable. An angle of one minute occupies, on the cir- 
cumference of a circle of 10 inches in radius, only about 
-g-J-oth part of an inch, a quantity too small to be certainly 
dealt with without the use of magnifying glasses ; yet one 
minute is a gross quantity in the astronomical measurement 
of an angle. With the instruments now employed in ob- 
servatories, a single second, or the 60th part of a minute, is 
rendered a distinctly visible and appreciable quantity. Now 
the arc of a circle, subtended by one second, is less than the 
200,000th part of the radius, so that on a circle of 6 feet in 
diameter it would occupy no greater linear extent than 7g 1 00 th 
part of an inch; a quantity requiring a powerful microscope 
to be discerned at all. Let any one figure to himself, there- 
fore, the difficulty of placing on the circumference of a me- 
tallic circle of such dimensions (supposing the difficulty of 
its construction surmounted), 360 marks, dots, or cognizable 
divisions, which shall all be true to their places within such 
narrow limits; to say nothing of the subdivision of the de- 
grees so marked off into minutes, and of these again into 
seconds. Such a work has probably baffled, and will proba- 
bly forever continue to baffle, the utmost stretch of human 
skill and industry; nor, if executed, could it endure. The 
ever varying fluctuations of heat and cold have a tendency 
to produce not merely temporary and transient, but per- 



112 OUTLINES OF ASTRONOMY 

manent, uncompensated changes of form in all considerable 
masses of those metals which alone are applicable to such 
uses ; and their own weight, however symmetrically formed, 
must always be unequally sustained, since it is impossible 
to apply the sustaining power to every part separately: even 
could this be done, at all events force must be used to move 
and to fix them; which can never be done without produc- 
ing temporary and risking permanent change of form. It is 
true, by dividing them on their centres, and in the identical 
places they are destined to occupy, and by a thousand in- 
genious and delicate contrivances, wonders have been ac- 
complished in this department of art, and a degree of per- 
fection has been given, not merely to chefs oVazuvre, but to 
instruments of moderate prices and dimensions, and in or- 
dinary use, which, on due consideration, must appear very 
surprising. But though we are entitled to look for wonders 
at the hands of scientific artists, we are not to expect mira- 
cles. The demands of the astronomer will always surpass 
the power of the artist ; and it must, therefore, be constantly 
the aim of the former to make himself, as far as possible, 
independent of the imperfections incident to every work the 
latter can place in his hands. He must, therefore, endeavor 
so to combine his observations, so to choose his opportuni- 
ties, and so to familiarize himself with all the causes which 
may produce instrumental derangement, and with all the 
peculiarities of structure and material of each instrument 
he possesses, as not to allow himself to be misled by their 
errors, but to extract from their indications, as far as possible, 
all that is true, and reject all that is erroneous. It is in this 
that the art of the practical astronomer consists — an art of 
itself of a curious and intricate nature, and of which we can 
here only notice some of the leading and general features. 



OUTLINES OF ASTRONOMY 113 

(132.) The great aim of the practical astronomer being 
numerical correctness in the results of instrumental meas- 
urement, his constant care and vigilance must be directed 
to the detection and compensation of errors, either by anni- 
hilating, or by taking account of, and allowing for them. 
Now, if we examine the sources from which errors may 
arise in any instrumental determination, we shall find them 
chiefly reducible to three principal heads:— 

(133.) 1st, External or incidental causes of error; com- 
prehending those which depend on external, uncontrollable 
circumstances: such as, fluctuations of weather, which dis- 
turb the amount of refraction from its tabulated value, and, 
being reducible to no fixed law, induce uncertainty to the 
extent of their own possible magnitude ; such as r by vary- 
ing the temperature of the air, vary also the form and posi- 
tion of the instruments used, by altering the relative mag- 
nitudes and the tension of their parts ; and others of the like 
nature. 

(134.) 2dly, Errors of observation : such as arise, for 
example, from inexpertness, defective vision, slowness in 
seizing the exact instant of occurrence of a phenomenon, or 
precipitancy in anticipating it, etc. ; from atmospheric indis- 
tinctness; insufficient optical power in the instrument, and 
the like. Under this head may also be classed all errors 
arising from momentary instrumental derangement — slips 
in clamping, looseness of screws, etc. 

(135.) 3dly, The third, and by far the most numerous 
class of errors to which astronomical measurements are 
liable, arise from causes which may be deemed instrumen- 
tal, and which may be subdivided into two principal classes. 
The first comprehends those which arise from an instrument 
not being what it professes to be, which is error of workman- 



Ill OUTLINES OF ASTRONOMY 

ship. Thus, if a pivot or axis;, instead of being, as it ought, 
exactly cylindrical, be slightly flattened, or elliptical — if it 
be not exactly (as it is intended it should be) concentric with 
the circle it carries; — if this circle (so called) be in reality 
not exactly circular, or not in one plane; — if its divisions, 
intended to be precisely equidistant, should be placed in 
reality at unequal intervals — and a hundred other things of 
the same sort. These are not mere speculative sources of 
error, but practical annoyances, which every observer has 
to contend with. 

(136.) The other subdivision of instrumental errors com- 
prehends such as arise from an instrument not being placed 
in the position it ought to have; and from those of its parts, 
which are made purposely movable, not being properly dis- 
posed inter se. These are errors of adjustment. Some are 
unavoidable, as they arise from a general unsteadiness of 
the soil or building in which the instruments are placed; 
which, though too minute to be noticed in any other way, 
become appreciable in delicate astronomical observations: 
others, again, are consequences of imperfect workmanship, 
as where an instrument once well adjusted will not remain 
so, but keeps deviating and shifting. But the most impor- 
tant of this class of errors arise from the non-existence of 
natural indications, other than those afforded by astronomi- 
cal observations themselves, whether an instrument has or 
has not the exact position, with respect to the horizon and 
its cardinal points, the axis of the earth, or to other prin- 
cipal astronomical lines and circles, which it ought to have 
to fulfil properly its objects. 

(137.) Now, with respect to the first two classes of error, 
it must be observed, that, in so far as they cannot be re- 
duced to known laws, and thereby become subjects of cal- 



OUTLINES OF ASTROROMY 115. 

dilation and due allowance, they actually vitiate, to their 
full extent, the results of any observations in which they 
subsist. Being, however, in their nature casual and acci- 
dental, their effects necessarily lie sometimes one way, 
sometimes the other; sometimes diminishing, sometimes 
tending to increase the results. Hence, by greatly multi- 
plying observations, under varied circumstances, by avoid- 
ing unfavorable, and taking advantage of favorable cir- 
cumstances of weather, or otherwise using opportunity to 
advantage — and finally, by taking the mean or average of 
the results obtained, this class of errors may be so far sub- 
dued, by setting them to destroy one another, as no longer 
sensibly to vitiate any theoretical or practical conclusion. 
This is the great and indeed only resource against such 
errors, not merely to the astronomer, but to the investi- 
gator of numerical results in every department of physical 
research. 

(138.) With regard to errors of adjustment and work- 
manship, not only the 'possibility, but the certainty of their 
existence, in every imaginable form, in all instruments, 
must be contemplated. Human hands or machines never 
formed a circle, drew a straight line, or erected a perpen- 
dicular, nor ever placed an instrument in perfect adjust- 
ment, unless accidentally; and then only during an instant 
of time. This does not prevent, however, that a great ap- 
proximation to all these desiderata should be attained. But 
it is the peculiarity of astronomical observation to be the 
ultimate means of detection of all mechanical defects which 
elude by their minuteness every other mode of detection. 
"What the eye cannot discern nor the touch perceive, a 
course of astronomical observations will make distinctly 
evident. The imperfect products of man's hands are here 



116 OUTLINES of: astronomy 

tested by being brought into comparison under very great 
magnifying powers (corresponding in effect to a great in- 
crease in acuteness of perception) with the perfect work- 
manship of nature; and there is none which will bear the 
trial. Now, it may seem like arguing in a vicious circle, to 
deduce theoretical conclusions and laws from observation, 
and then to turn round upon the instruments with which 
those observations were made, accuse them of imperfection, 
and attempt to detect and rectify their errors by means of 
the very laws and theories which they have helped us to 
a knowledge of. A little consideration, however, will suf- 
fice to show that such a course of proceeding is perfectly 
legitimate. 

(139.) The steps by which we arrive at the laws of 
natural phenomena, and especially those which depend for 
their verification on numerical determinations, are necessa- 
rily successive. Gross results and palpable laws are arrived 
at by rude observation with coarse instruments, or without 
any instruments at all, and are expressed in language which 
is- not to be considered as absolute, but is to be interpreted 
with a degree of latitude commensurate to the imperfection 
of the observations themselves. These results are corrected 
and refined by nicer scrutiny, and with more delicate means. 
The first rude expressions of the laws which embody them 
are perceived to be inexact. The language used in their 
expression is corrected, its terms more rigidly defined, or 
fresh terms introduced, until the new state of language and 
terminology is brought to fit the improved state of knowl- 
edge of facts. In the progress of this scrutiny subordinate 
laws are brought into view which still further modify, both 
the verbal statement and numerical results of those which 
first offered themselves to our notice ; and when these are 



OUTLINES OF ASTRONOMY 117 

traced out and reduced to certainty, others, again, subordi- 
nate to them, make their appearance, and become subjects 
of further inquiry. Now, it invariably happens (and the 
reason is evident) that the first glimpse we catch of such 
subordinate laws — the first form in which they are dimly 
shadowed out to our minds — is that of errors. We per- 
ceive a discordance between what we expect, and what we 
find. The first occurrence of such a discordance we attrib- 
ute to accident. It happens again and again; and we begin 
to suspect our instruments. We then inquire, to what 
amount of error their determinations can, by possibility, be 
liable. If their limit of possible error exceed the observed 
deviation, we at once condemn the instrument, and set 
about improving its construction or adjustments. Still the 
same deviations occur, and, so far from being palliated, 
are more marked and better defined than before. We are 
now sure that we are on the traces of a law of nature, and 
we pursue it till we have reduced it to a definite state- 
ment, and verified it by repeated observation, under every 
variety of circumstances. 

(140.) Now, in the course of this inquiry, it will not fail 
to happen that other discordances will strike us. Taught 
by experience, we suspect the existence of some natural 
law, before unknown; we tabulate {i.e. draw out in order) 
the results of our observations; and we perceive, in this 
synoptic statement of them, distinct indications of a regular 
progression. Again we improve or vary our instruments, 
and we now lose sight of this supposed new law of nature 
altogether, or find it replaced by some other, of a totally 
different character. Thus we are led to suspect an instru- 
mental cause for what we have noticed. We examine, 
therefore, the theory of our instrument; we suppose defects 



118 OUTLINES OF ASTRONOMY 

in its structure, and, by the aid of geometry, we trace their 
influence in introducing actual errors into its indications. 
These errors have their laws, which, so long as we have 
no knowledge of causes to guide us, may be confounded 
with laws of nature, as they are mixed up with them in 
their effects. They are not fortuitous, like errors of obser- 
vation, but, as they arise from sources inherent in the in- 
strument, and unchangeable while it and its adjustments 
remain unchanged, they are reducible to fixed and ascer- 
tainable forms ; each particular defect, whether of structure 
or adjustment, producing its own appropriate form of error. 
When these are thoroughly investigated, we recognize 
among them one which coincides in its nature and pro- 
gression with that of our observed discordances. The 
mystery is at once solved. "We have detected, by direct 
observation, an instrumental defect. 

(141.) It is, therefore, a chief requisite for the practical 
astronomer to make himself completely familiar with the 
theory of his instruments. By this alone is he enabled at 
once to decide what effect on his observations any given 
imperfection of structure or adjustment will produce in any 
given circumstances under which an observation can be 
made. This alone also can place him in a condition to derive 
available and practical means of destroying and eliminating 
altogether the influence of such imperfections, by so arrang- 
ing his observations, that it shall affect their results in op- 
posite ways, and that its influence shall thus disappear 
from their mean, which is one of the chief modes by which 
precision is attained in practical astronomy. Suppose, for 
example, the principle of an instrument required that a 
circle should be concentric with the axis on which it is 
made to turn. As this is a condition which no workman- 



OUTLINES OF ASTRONOMY 119 

ship can exactly fulfil, it becomes necessary to inquire what 
errors will be produced in observations made and registered 
on the faith of such an instrument, by any assigned devia- 
tion in this respect; that is to say, what would be the dis- 
agreement between observations made with it and with one 
absolutely perfect, could such be obtained. Now, simple 
geometrical considerations suffice to show — 1st, that if the 
axis be excentric by a given fraction (say one thousandth 
part) of the radius of the circle, all angles read off on that 
part of the circle toward which the excentricity lies, will 
appear by that fractional amount too small, and all on the 
opposite side too large. And, 2dly, that whatever be the 
amount of the excentricity, and on whatever part of the cir- 
cle any proposed angle is measured, the effect of the error 
in question on the result of observations depending on the 
graduation of its circumference (or limb, as it is technically 
called) will be completely annihilated by the very easy 
method of always reading off the divisions on two diamet- 
rically opposite points of the circle, and taking a mean ; for 
the effect of excentricity is always to increase the arc repre- 
senting the angle in question on one side of the circle, by 
just the same quantity by which it diminishes that on the 
other. Again, suppose that the proper use of the instru- 
ment required that this axis should be exactly parallel 
to that of the earth. As it never can be placed or remain 
so, it becomes a question, what amount of error will arise, 
in its use, from any assigned deviation, whether in a hori- 
zontal or vertical plane, from this precise position. Such 
inquiries constitute the theory of instrumental errors ; a the- 
ory of the utmost importance to practice, and one of which 
a complete knowledge will enable an observer, with moder- 
ate instrumental means, often to attain a degree of precision 



120 OUTLINES OF ASTRONOMY 

which might seem to belong only to the most refined and 
costly. This theory, as will readily be apprehended, turns 
almost entirely on considerations of pure geometry, and 
those for the most part not difficult. In the present work, 
however, we have no further concern with it. The astro- 
nomical instruments we propose briefly to describe in this 
chapter will be considered as perfect both in construction 
and adjustment. 2 

(142.) As the above remarks are very essential to a 
right understanding of the philosophy of our subject and 
the spirit of astronomical methods, we shall elucidate them 
by taking one or two special cases. Observant persons, be- 
fore the invention of astronomical instruments, had already 
concluded the apparent diurnal motions of the stars to be 
performed in circles about fixed poles in the heavens, as 
shown in the foregoing chapter. In drawing this conclu- 
sion, however, refraction was entirely overlooked, or, if 
forced on their notice by its great magnitude in the im- 
mediate neighborhood of the horizon, was regarded as a 
local irregularity, and, as such, neglected or slurred over. 
As soon, however, as the diurnal paths of the stars were 
attempted to be traced by instruments, even of the coarsest 
kind, it became evident that the notion of exact circles de- 
scribed about one and the same pole would not represent 
the phenomena correctly, but that, owing to some cause or 
other, the apparent diurnal orbit of every star is distorted 
from a circular into an oval form, its lower segment being 
flatter than its upper; and the deviation being greater the 



2 The principle on which the chief adjustments of two or three of the most 
useful and common instruments, such as the transit, the equatorial, and the 
sextant, are performed, are, however, noticed, for the convenience of readers 
who may use such instruments without going further into the arcana of prac- 
tical astronomy. 



OUTLINES OF ASTRONOMY 121 

nearer the star approached the horizon, the effect being the 
same as if the circle had been squeezed upward from be- 
low, and the lower parts more than the higher. For such 
an effect, as it was soon found to arise from no casual or 
instrumental cause, it became necessary to seek a natural 
one; and refraction readily occurred, to solve the difficulty. 
In fact, it is a case precisely analogous to what we have 
already noticed (art. 47), of the apparent distortion of the 
sun near the horizon, only on a larger scale, and traced 
up to greater altitudes. This new law once established, it 
became necessary to modify the expression of that anciently 
received, by inserting in it a salvo for the effect of refrac- 
tion, or by making a distinction between the apparent di- 
urnal orbits, as affected by refraction, and the true ones 
cleared of that effect. This distinction between the ap- 
parent and the true — between the uncorrected and corrected — 
between the rough and obvious, and the refined and ultimate 
— is of perpetual occurrence in every part of astronomy. 

(143.) Again. The first impression produced by a view 
of the diurnal movement of the heavens is that all the 
heavenly bodies perform this revolution in one common 
period, viz., a day, or 24 hours. But no sooner do we 
come to examine the matter instrumentality, i.e. by noting, 
by timekeepers, their successive arrivals on the meridian, 
than we find differences which cannot be accounted for by 
any error of observation. All the stars, it is true, occupy 
the same interval of time between their successive appulses 
to the meridian, or to any vertical circle; but this is a very 
different one from that occupied by the sun. It is palpa- 
bly shorter; being, in fact, only 23 h 56' 4-09", instead of 
24 hours, such hours as our common clocks mark. Here, 

then, we have already two different days, a sidereal and a 
Astronomy — Vol. XIX. — 6 



122 OUTLINES OF ASTRONOMY 

solar; and if, instead of tne sun, we observe the moon, we 
find a third, much longer than either — a lunar day, whose 
average duration is 24 h 54 m of our ordinary time, which 
last is solar time, being of necessity conformable to the 
sun's successive reappearances, on which all the business 
of life depends. 

(144.) Now, all the stars are found to be unanimous in 
giving the same exact duration of 23 h 56' 4-09", for the 
sidereal day; which, therefore, we cannot hesitate to receive 
as the period in which the earth makes one revolution on 
its axis. We are, therefore, compelled to look on the sun 
and moon as exceptions to the general law; as having a 
different nature, or at least a different relation to us, from 
the stars; and as having motions, real or apparent, of their 
own, independent of the rotation of the earth on its axis. 
Thus a great and most important distinction is disclosed 
to us. 

(145.) To establish these facts, almost no apparatus is 
required. An observer need only station himself to the 
north of some well-defined vertical object, as the angle of 
a building, and, placing his eye exactly at a certain fixed 
point (such as a small hole in a plate of metal nailed to 
some immovable support), notice the successive disappear- 
ances of any star behind the building, by a watch. 3 When 
he observes the sun, he must shade his eye with a dark- 
colored or smoked glass, and notice the moments when its 



3 This is an excellent practical method of ascertaining the rate of a clock or 
watch, being exceedingly accurate if a few precautions are attended to ; the 
chief of which is, to take care that that part of the edge behind which the star 
(a bright one, not a planet) disappears shall be quite smooth ; as otherwise vari- 
able refraction may transfer the point of disappearance from a protuberance to 
a notch, and thus vary the moment of observation unduly <, This is easily se- 
cured, by nailing up a smooth- edged board. The vertically of its edge should 
be insured by the use of a plumb -line. 



OUTLINES OF ASTRONOMY 123 

western and eastern edges successively come tip to the wall, 
from which, by taking half the interval, he will ascertain 
(what he cannot directly observe) the moment of disappear- 
ance of its centre. 

(146.) When, in pursuing and establishing this general 
fact, we are led to attend more nicely to the times of the 
daily arrival of the sun on the meridian, irregularities (such 
they first seem to be) begin to make their appearance. The 
intervals between two successive arrivals are not the same 
at all times of the year. They are sometimes greater, some- 
times less, than 24 hours, as shown by the clock; that is to 
say, the solar day is not always of the same length. About 
the 21st of December, for example, it is half a minute 
longer, and about the same day of September nearly as 
much shorter, than its average duration. And thus a dis- 
tinction is again pressed upon our notice between the 
actual solar day, which is never two days in succession 
alike, and the mean solar day of 24 hours, which is an 
average of all the solar days throughout the year. Here, 
then, a new source of inquiry opens to us. The sun's ap- 
parent motion is not only not the same with that of the 
stars, but it is not (as the latter is) uniform. It is subject 
to fluctuations, whose laws become matter of investigation. 
But to pursue these laws, we require nicer means of obser- 
vation than what we have described, and are obliged to call 
in to our aid an instrument called the transit instrument, 
especially destined for such observations, and to attend 
minutely to all the causes of irregularity in the going of 
clocks and watches which may affect our reckoning of 
time. Thus we become involved by degrees in more and 
more delicate instrumental inquiries; and we speedily find 
that, in proportion as we ascertain the amount and law 



124 OUTLINES OF ASTRONOMY 

of one great or leading fluctuation, or inequality, as it is 
called, of the sun's diurnal motion, we bring into view 
others continually smaller and smaller, which were before 
obscured, or mixed up with errors of observation and in- 
strumental imperfections. In short, we may not inaptly 
compare the mean length of the solar day to the mean or 
average height of water in a harbor, or the general level 
of the sea unagitated by tide or waves. The great annual 
fluctuation above noticed may be compared to the daily 
variations of level produced by the tides, which are noth» 
ing but enormous waves extending over the whole ocean, 
while the smaller subordinate inequalities may be assimi- 
lated to waves ordinarily so called, on which, when large, 
we perceive lesser undulations to ride, and on these, again, 
minuter ripplings, to the series of whose subordination we 
can perceive no end. 

(147.) With the causes of these irregularities in the solar 
motion we have no concern at present; their explanation 
belongs to a more advanced part of our subject: but the 
distinction between the solar and sidereal days, as it per- 
vades every part of astronomy, requires to be early intro- 
duced, and never lost sight of. It is, as already observed, 
the mean or average length of the solar day, which is used 
in the civil reckoning of time. It commences at midnight, 
but astronomers, even when they use mean solar time, de- 
part from the civil reckoning, commencing their day at 
noon, and reckoning the hours from round to 24. Thus, 
11 o'clock in the forenoon of the second of January, in the 
civil reckoning of time, corresponds to January 1 day 23 
hours in the astronomical reckoning; and 1 o'clock in 
the afternoon of the former, to January 2 days 1 hour 
of the latter reckoning. This usage has its advantages and 



OUTLINES OF ASTRONOMY 125 

disadvantages, but the latter seem to preponderate; and it 
would be well if, in consequence, it could be broken 
through, and the civil reckoning substituted. Uniformity 
in nomenclature and modes of reckoning in all matters relat- 
ing to time, space, weight, measure, etc., is of such vast and 
paramount importance in every relation of life as to outweigh 
every consideration of technical convenience or custom.* 

(148.) Both astronomers and civilians, however, who 
inhabit different points of the earth's surface, differ from 
each other in their reckoning of time; as it is obvious they 
must, if we consider that, when it is noon at one place, it 
is midnight at a place diametrically opposite; sunrise at 
another; and sunset, again, at a fourth. Hence arises con- 
siderable inconvenience, especially as respects places differ- 
ing very widely in situation, and which may even in some 
critical cases involve the mistake of a whole day. To ob- 
viate this inconvenience, there has lately been introduced 
a system of reckoning time by mean solar days and parts 
of a day counted from a fixed instant, common to all the 
world, and determined by no local circumstance, such as 
noon or midnight, but by the motion of the sun among 
the stars. Time, so reckoned, is called equinoctial time; 
and is numerically the same, at the same instant, in every 
part of the globe. Its origin will be explained more fully 
at a more advanced stage of our work. 



4 The only disadvantage to astronomers of using the civil reckoning is this 
— that their observations being chiefly carried on during the night, the day of 
their date will, in this reckoning, always have to be changed at midnight, and 
the former and latter portion of every night's observations will belong to two 
differently numbered civil days of the month. There is no denying this to be 
an inconvenience. Habit, however, would alleviate it; arid some inconveniences 
must be cheerfully submitted to by all who resolve to act on general principles. 
All other classes of men, whose occupation extends to the night as well as day, 
submit to it, and find their advantage in doing so. 



126 OUTLINES OF ASTRONOMY 

(149.) Time is an essential element in astronomical ob- 
servation, in a twofold point of view: — 1st, As the represen- 
tative of angular motion. The earth's diurnal motion being 
uniform, every star describes its diurnal circle uniformly; 
and the time elapsing between the passage of the stars in 
succession across the meridian of any observer becomes, 
therefore, a direct measure of their differences of right 
ascension. 2dly, As the fundamental element (or natural 
independent variable, to use the language of geometers) in 
all dynamical theories. The great object of astronomy is 
the determination of the laws of the celestial motions, and 
their reference to their proximate or remote causes. Now, 
the statement of the law of any observed motion in a celes- 
tial object can be no other than a proposition declaring what 
has been, is, and will be, the real or apparent situation of 
that object at any time, past, present, or future. To com- 
pare such laws, therefore, with observation, we must possess 
a register of the observed situations of the object in ques- 
tion, and of the times when they were observed. 

(150.) The measurement of time is performed by clocks, 
chronometers, clepsydras, and hour-glasses. The two former 
are alone used in modern astronomy. The hour-glass is a 
coarse and rude contrivance for measuring, or rather count- 
ing out, fixed portions of time, and is entirely disused. The 
clepsydra, which measured time by the gradual emptying 
of a large vessel of water through a determinate orifice, is 
susceptible of considerable exactness, and was the only 
dependence of astronomers before the invention of clocks 
and watches. At present it is abandoned, owing to the 
greater convenience and exactness of the latter instruments. 
In one case only has the revival of its use been proposed; 
viz., for the accurate measurement of very small portions 



OUTLINES OF ASTRONOMY 12T 

of time, by the flowing out of mercury from a small orifice 
in the bottom of a vessel, kept constantly full to a fixed 
height. The stream is intercepted at the moment of noting 
any event, and directed aside into a receiver, into which it 
continues to run, till the moment of noting any other event, 
when the intercepting cause is suddenly removed, the stream 
flows in its original course, and ceases to run into the re- 
ceiver. The weight of mercury received, compared with the 
weight received in an interval of time observed by the 
clock, gives the interval between the events observed. 
This ingenious and simple method of resolving, with all 
possible precision, a problem of much importance in many 
physical inquiries, is due to the late Captain Kater. 

(151.) The pendulum clock, however, and the balance 
watch, with those improvements and refinements in its 
structure which constitute it emphatically a chronometer,* 
are the instruments on which the astronomer depends for 
his knowledge of the lapse of time. These instruments 
are now brought to such perfection, that a habitual irreg- 
ularity in the rate of going, to the extent of a single second 
in twenty-four hours in two consecutive days, is not toler- 
ated in one of good character; so that any interval of time 
less than twenty -four hours may be certainly ascertained 
within a few tenths of a second, by their use. In proportion 
as intervals are longer, the risk of error, as well as the 
amount of error risked, becomes greater, because the acci- 
dental errors of many days may accumulate; and causes 
producing a slow progressive change in the rate of going 
may subsist unperceived. It is not safe, therefore, to trust 
the determination of time to clocks, or watches, for many 

6 Xpovos, time; ixerpeiv, to measure. 



128 OUTLINES OF ASTRONOMY 

days in succession, without checking them, and ascertaining 
their errors by reference to natural events which we know 
to happen, day after day, at equal intervals. But if this 
be done, the longest intervals may be fixed with the same 
precision as the shortest; since, in fact, it is then only the 
times intervening between the first and the last moments of 
such long intervals, and such of those periodically recurring 
events adopted for our points of reckoning, as occur within 
twenty- four hours respectively of either, which we measure 
by artificial means. The whole days are counted out for us 
by nature ; the fractional parts only, at either end, are meas- 
ured by our clocks. To keep the reckoning of the integer 
days correct, so that none shall be lost or counted twice, is 
the object of the calendar. Chronology marks out the order 
of succession of events, and refers them to their proper years 
and days; while chronometry, grounding its determinations 
on the precise observation of such regularly periodical events 
as can be conveniently and exactly subdivided, enables us to 
fix the moments in which phenomena occur, with the last 
degree of precision. 

(152.) In the culmination or transit (i.e. the passage across 
the meridian of an observer) of every star in the heavens, he 
is furnished with such a regularly periodical natural event 
as we allude to. Accordingly, it is to the transits of the 
brightest and most conveniently situated fixed stars that 
astronomers resort to ascertain their exact time, or, which 
comes to the same thing, to determine the exact amount 
of error of their clocks. 

(153.) Before we describe the instrument destined for 
the purpose of observing such culminations, however, or 
those intended for the measurement of angular intervals in 
the sphere, it is requisite to place clearly before the reader 



OUTLINES OF ASTRONOMY 129 

the principle on which the telescope is applied in astronomy 
to the precise determination of a direction in space — that, 
namely, of the visual ray by which we see a star or any 
other distant object. 

(154.) The telescope most commonly used in astronomy 
for these purposes is the refracting telescope, which consists 
of an object-glass (either single, or as is now almost univer- 
sal, double, forming what is called in optics, an achromatic 
combination) A; a tube AB, into which the brass cell of the 
object-glass is firmly screwed, and an eye-lens C, for which 
is often substituted a combination of glasses designed to in- 




crease the magnifying power of the telescope, or otherwise 
give more distinctness of vision according to optical prin- 
ciples which we have no occasion here to refer to. This 
also is fitted into a cell, which is screwed firmly into the 
end B of the tube, so that object-glass, tube, and eye-glass 
may be considered as forming one piece, invariable in the 
relative position of its parts. 

(155.) The line P Q joining the centres of the object and 
eye-glasses and produced, is called the axis or line of collima- 
tion of the telescope. And it is evident, that the situation 
of this line holds a fixed relation to the tube and its appen- 
dages, so long as the object and eye-glasses maintain their 
fixity in this respect. 

(156.) Whatever distant object E this line is directed to, 
an inverted picture or image of that object F is formed 
(according to the principles of optics), in the focus of the 
object-glass, and may there be viewed as if it were a real 



130 OUTLINES OF ASTRONOMY 

object, through the eye-lens C, which (if of short focus) en- 
ables us to magnify it just as such a lens would magnify a 
material object in the same place. 

(157.) Now as this image is formed and viewed in the 
air, being itself immaterial and impalpable — nothing pre- 
vents our placing in that very place F in the axis of the 
telescope, a real, substantial object of very definite form and 
delicate make, such as a fine metallic point, as of a needle — 
or better still, a cross formed by two very fine threads 
(spider- lines), thin metallic wires, or lines drawn on glass 
intersecting each other at right angles — and whose intersec- 
tion is all but a mathematical point. If such a point, wire, 
or cross be carefully placed and firmly fixed in the exact 
focus F, both of the object and eye-glass, it will be seen 
through the latter at the same time, and occupying the same 
precise place as the image of the distant star E. The mag- 
nifying power of the lens renders perceptible the smallest 
deviation from perfect coincidence, which, should it exist, 
is a proof, that the axis Q P is not directed rigorously 
toward E. In that case, a fine motion (by means of a screw 
duly applied), communicated to the telescope, will be neces- 
sary to vary the direction of the axis till the coincidence is 
rendered perfect. So precise is this mode of pointing found 
in practice, that the axis of a telescope may be directed 
toward a star or other definite celestial object without an 
error of more than a few tenths of a second of angular 
measure. 

(158.) This application of the telescope may be consid- 
ered as completely annihilating that part of the error of 
observation which might otherwise arise from an erroneous 
estimation of the direction in which an object lies from the 
observer's eye, or from the centre of the instrument. It is, 



OUTLINES OF ASTRONOMY 131 

in fact, the grand source of all the precision of modern as- 
tronomy, without which all other refinements in instrumen- 
tal workmanship would be thrown away; the errors capable 
of being committed in pointing to an object, without such 
assistance, being far greater than what could arise from any 
but the very coarsest graduation. 6 In fact, the telescope 
thus applied becomes, with respect to angular, what the 
microscope is with respect to linear dimension. By concen- 
trating attention on its smallest parts, and magnifying into 
palpable intervals the minutest differences, it enables us 
not only to scrutinize the form and structure of the objects 
to which it is pointed, but to refer their apparent places, 
with all but geometrical precision, to the parts of any scale 
with which we propose to compare them. 

(159). We now return to our subject, the determination 
of time by the transit or culminations of celestial objects. 
The instrument with which such culminations are observed 
is called a transit instrument. It consists of a telescope 



6 The honor of this capital improvement has been successfully vindicated by 
Derham (Phil. Trans, xxx. 603) to our young, talented and unfortunate country- 
man G-ascoigne, from his correspondence with Crabtree and Horrockes, in his 
(Derham's) possession. The passages cited by Derham from these letters leave 
no doubt that, so early as 1640, G-ascoigne had applied telescopes to his quad- 
rants and sextants, with threads in the common focus of the glasses; and had 
even carried the invention so far as to illuminate the field of view by artificial 
light, which he found "very helpful when the moon appeareth not, or it is not 
otherwise light enough. ' ' These inventions were freely communicated by him 
to Crabtree, and through him to his friend Horrockes, the pride and boast of 
British astronomy; both of whom expressed their unbounded admiration of this 
and many other of his delicate and admirable improvements in the art of obser- 
vation. G-ascoigne, however, perished at the age of twenty-three, at the battle 
of Marston Moor; and the premature and sudden death of Horrockes, at a yet 
earlier age, will account for the temporary oblivion of the invention. It was 
revived, or re-invented, in 1667, by Picard and Auzout (Lalande, Astron. 2310), 
after which its use became universal. Morin, even earlier than Gascoigne (in 
1635), had proposed to substitute the telescope for plain sights; but it is the 
thread or wire stretched in the focus with which the image of a star can be 
brought to exact coincidence, which gives the telescope its advantage in prac- 
tice; and the idea of this does not seem to have occurred to Morin. (See 
Lalande, ubi supra.) 



132 OUTLINES OF ASTRONOMY 

firmly fastened on a horizontal axis directed to the east 
and west points of the horizon, or at right angles to the 
plane of the meridian of the place of observation. The 
extremities of the axis are formed into cylindrical pivots 
of exactly equal diameters, which rest in notches formed in 
metallic supports, bedded (in the case of large instruments) 
on strong pieces of stone, and susceptible of nice adjustment 
by screws, both in a vertical and horizontal direction. By 
the former adjustment, the axis can be rendered precisely 
horizontal, by levelling it with a level made to rest on 
By the latter adjustment the axis is brought 
precisely into the east and west direc- 
tion, the criterion of which is furnished 
nl^^ bv the observations themselves made with 

fi \\ \ ^ e i nstrument > i n a manner presently to 
be explained, or by a well-defined object, 
called a meridian mark, originally deter- 
mined by such observations, and then, for convenience 
of ready reference, permanently established, at a great dis- 
tance, exactly in a meridian line passing through the central 
point of the whole instrument. It is evident, from this 
description, that, if the axis, or line of collimation of the 
telescope, be once well adjusted at right angles to the axis 
of the transit, it will never quit the plane of the meridian, 
when the instrument is turned round on its axis of rotation. 
(160). In the focus of the eye-piece, and at right angles 
to the length of the telescope, is placed, not a single cross, 
as in our general explanation in art. 157, but a system of 
one horizontal and several equidistant vertical threads or 
wires (five or seven are more usually employed), as repre- 
sented in the annexed figure, which always appear in the 
field of view, when properly illuminated by day by the light 





OUTLINES OF ASTRONOMY 133 

of the sky, by night by that of a lamp introduced by a con- 
trivance not necessary here to explain. The place of this 
system of wires may be altered by adjusting screws, giving 
it a lateral (horizontal) motion; and it is by this means 
brought to such a position, that the middle one of the ver- 
tical wires shall intersect the line of collimation of the tele- 
scope, where it is arrested and permanently fastened. 7 In 
this situation it is evident that the middle thread will be a 
visible representation of that portion of the celestial merid- 
ian to which the telescope is pointed: and when a star is 
seen to cross this wire in the telescope, it 
is in the act of culminating, or passing the 
celestial meridian. The instant of this event 
is noted by the clock or chronometer, which 
forms an indispensable accompaniment of the 
transit instrument. For greater precision, the moments of 
its crossing all the vertical threads is noted; and a mean 
taken, which (since the threads are equidistant) would give 
exactly the same result, were all the observations perfect, 
and will of course, tend to subdivide and destroy their 
errors in an average of the whole in the contrary case. 

(161.) For the mode of executing the adjustments, and 
allowing for the errors unavoidable in the use of this sim- 
ple and elegant instrument, the reader must consult works 
especially devoted to this department of practical astron 
omy. 8 We shall here only mention one important verifica- 
tion of its correctness, which consists in reversing the ends 

7 There is no way of bringing the true optic axis of the object-glass to coin- 
cide exactly with the line of collimation, but, so long as the object-glass does 
not shift or shake in its cell, any line holding an invariable position with re- 
spect to that axis, may be taken for the conventional or astronomical axis with 
equal effect. 

8 See Dr. Pearson's Treatise on Practical Astronomy. Also Bianchi Sopra 
lo Stromento de' Passagi. Bphem. di Milano, 1824. 



134 OUTLINES OF ASTRONOMY 

of the axis, or turning it east for west. If this be done, and 
it continue to give the same results, and intersect the same 
point on the meridian mark, we may be sure that the line 
of collimation of the telescope is truly at right angles to the 
axis, and describes strictly a plane, i. e. marks out in the 
heavens a great circle. In good transit observations, an 
error of one or two -tenths of a second of time in the moment 
of a star's culmination is the utmost which need be appre- 
hended, exclusive of the error of the clock: in other words, 
a clock may be compared with the earth's diurnal motion 
by a single observation, without risk of greater error. By 
multiplying observations, of course, a yet greater degree of 
precision may be obtained. 

(162). The plane described by the line of collimation of 
a transit ought to be that of the meridian of the place of 
observation. To ascertain whether it is so or not, celestial 
observation must be resorted to. Now, as the meridian is a 
great circle passing through the pole, it necessarily bisects 
the diurnal circles described by all the stars, all which de- 
scribe the two semicircles so arising in equal intervals of 
12 sidereal hours each. Hence, if we choose a star whose 
whole diurnal circle is above the horizon, or which never 
sets, and observe the moments of its upper and lower tran- 
sits across the middle wire of the telescope, if we find the 
two semidiurnal portions east and west of the plane de- 
scribed by the telescope to be described in precisely equal 
times, we may be sure that plane is the meridian. 

(163.) The angular intervals measured by means of the 
transit instrument and clock are arcs of the equinoctial, in- 
tercepted between circles of declination passing through the 
objects observed; and their measurement, in this case, is 
performed by no artificial graduation of circles, but by the 



OUTLINES OF ASTRONOMY 135 

help of the earth's diurnal motion, which, carries equal arcs 
of the equinoctial across the meridian, in equal times, at 
the rate of 15° per sidereal hour. In all other cases, when 
we would measure angular intervals, it is necessary to have 
recourse to circles, or portions of circles, constructed of 
metal or other firm and durable material, and mechanically 
subdivided into equal parts, such as degrees, minutes, etc. 
The simplest and most obvious mode in which the measure- 
ment of the angular interval between two directions in space 
can be performed is as follows. Let A B C D be a circle, 
divided into 360 degrees (numbered in order from any point 
0° in the circumference, round to the same point again), and 
connected with its centre by 
spokes or rays, as, y 1 z, firmly 
united to its circumference or 
limb. At the centre let a 
circular hole be pierced, in 
which shall move a pivot 
exactly fitting it, carrying a 
tube, whose axis, a &, is ex- 
actly parallel to the plane of the circle, or perpendicular to 
the pivot ; and also two arms, m, n, at right angles to it, and 
forming one piece with the tube and the axis ; so that the mo- 
tion of the axis on the centre shall carry the tube and arms 
smoothly round the circle, to be arrested and fixed at any 
point we please, by a contrivance called a clamp. Suppose, 
now, we would measure the angular interval between two 
fixed objects, S, T. The plane of the circle must first be 
adjusted so as to pass through them both, and immovably 
fixed and maintained in that position. This done, let the 
axis a b of the tube be directed to one of them, S, and 
clamped. Then will a mark on the arm m point either ex- 




136 



OUTLINES OF ASTRONOMY 



actly to some one of the divisions on the limb, or between 
two of them adjacent. In the former case, the division 
must be noted as the reading of the arm m. In the latter, 
the fractional part of one whole interval between the con- 
secutive divisions by which the mark on m surpasses the 
last inferior division must be estimated or measured by 
some mechanical or optical means. (See art. 165.) The 
division and fractional part thus noted, and reduced into 
degrees, minutes, and seconds, is to be set down as the 
reading of the limb corresponding to that position of the tube 
a b, where it points to the object S. The same must then 
be done for the object T; the tube pointed to it, and the 
limb "read off," the position of the circle remaining mean- 
while unaltered. It is manifest, then, that, if the lesser of 
these readings be subtracted from the greater, their difference 
will be the angular interval between S and T, as seen from 
the centre of the circle, at whatever point of the limb the 
commencement of the graduations or the point 0° be 
situated. 

(164.) The very same result will be obtained, if, instead 
of making the tube movable upon the circle, we connect it 




invariably with the latter, and make both revolve together 
on an axis concentric with the circle, and forming one piece 
with it, working in a hollow formed to receive and fit it in 



OUTLINES OF ASTRONOMY 



187 



some fixed support. Such a combination is represented in 
section in the above sketch. T is the tube or sight, fast- 
ened, &tpp, on the circle A B, whose axis, D, works in the 
solid metallic centring E, from which originates an arm, F, 
carrying at its extremity an index, or other proper mark, to 
point out and read off the exact division of the circle at B, 
the point close to it. It is evident that, as the telescope 
and circle revolve through any angle, the part of the limb 
of the latter, which by such revolution is carried past the 
index F, will measure the angle described. This is the 
most usual mode of applying divided circles in astronomy. 
(165.) The index F may either be a simple pointer, like 
a clock hand {fig. a); or a vernier {fig. h); or, lastly, a com- 



^s^ 





pound microscope {fig. c), represented in section in fig. d, 
and furnished with a cross in the common focus of its object 
and eye-glass, movable by a fine-threaded screw, by which 
the intersection of the cross may be brought to exact coin- 
cidence with the image of the nearest of the divisions of the 
circle formed in the focus of the object lens upon the very 
same principle with that explained, art. 157, for the point- 
ing of the telescope, only that here the fiducial cross is made 
movable ; and by the turns and parts of a turn of the screw 
required for this purpose the distance of that division from 
the original or zero point of the microscope may be esti- 
mated. This simple but delicate contrivance gives to the 



138 OUTLINES OF ASTRONOMY 

reading off of a circle a degree of accuracy only limited by 
the power of the microscope and the perfection with which 
a screw can be executed, and places the subdivision of 
angles on the same footing of optical certainty which is 
introduced into their measurement by the use of the tele- 
scope. 

(166.) The exactness of the result thus obtained must 
depend, 1st, on the precision with which the tube a b can 
be pointed to the objects ; 2dly, on the accuracy of gradua- 
tion of the limb; 3dly, on the accuracy with which the sub- 
division of the intervals between any two consecutive grad- 
uations can be performed. The mode of accomplishing the 
latter object with any required exactness has been explained 
in the last article. With regard to the graduation of the 
limb, being merely of a mechanical nature, we shall pass 
it without remark, further than this, that, in the present 
state of instrument-making, the amount of error from this 
source of inaccuracy is reduced within very narrow limits 
indeed. 9 With regard to the first, it must be obvious that, 
if the sights a b be nothing more than simple crosses, or 
pin-holes at the ends of a hollow tube, or an eye-hole 
at one end, and a cross at the other, no greater nicety in 
pointing can be expected than what simple vision with the 
naked eye can command. But if, in place of these simple 
but coarse contrivances, the tube itself be converted into 
a telescope, having an object-glass at b, an eye-piece at a, 
and a fiducial cross in their common focus, as explained 
in art. 157; and if the motion of the tube on the limb of 
the circle be arrested when the object is brought just into 



9 In the great Ertel circle at Pulkova, the probable amount of the accidental 
error of division is stated by M. Struve not to exceed 0" , 264. Desc. de l'Obs. 
centrale de Pulkova, p. 147. 



OUTLINES OF ASTRONOMY 139 

coincidence with the intersectional point of that cross, it is evi- 
dent that a greater degree of exactness may be attained in the 
pointing of the tube than by the unassisted eye, in proportion 
to the magnifying power and distinctness of the telescope used. 
(167.) The simplest mode in which the measurement of 
an angular interval can be executed, is what- we have just 
described; but, in strictness, this mode is applicable only 
to terrestrial angles, such as those occupied on the sensible 
horizon by the objects which surround our station — because 
these only remain stationary during the interval while the 
telescope is shifted on the limb from one object to the 
other. But the diurnal motion of the heavens, by destroy- 
ing this essential condition, renders the direct measurement 
of angular distance from object to object by this means im- 
possible. The same objection, however, does not apply if 
we seek only to determine the interval between the diurnal 
circles described by any two celestial objects. Suppose 
every star, in its diurnal revolution, were to leave behind 
it a visible trace in the heavens — a fine line of light, for in- 
stance — then a telescope once pointed to a star, so as to 
have its image brought to coincidence with the intersection 
of the wires, would constantly remain pointed to some por- 
tion or other of this line, which would therefore continue 
to appear in its field as a luminous line, permanently inter- 
secting the same point, till the star came round again. 
From one such line to another the telescope might be 
shifted, at leisure, without error; and then the angular 
interval between the two diurnal circles, in the plane of the 
telescope 1 s rotation, might be measured. Now, though we 
cannot see the path of a star in the heavens, we can wait 
till the star itself crosses the field of view, and seize the 
moment of its passage to place the intersection of its wires 



1-iO OUTLINES OF ASTRONOMY 

so that the star shall traverse it; by which, when the tele- 
scope is well clamped, we equally well secure the position 
of its diurnal circle as if we continued to see it ever so 
long. The reading off of the limb may then be performed 
at leisure; and when another star comes round into the plane 
of the circle, we may unclamp the telescope, and a similar 
observation will enable us to assign the place of its diurnal 
circle on the limb: and the observations may be repeated 
alternately, every day, as the stars pass, till we are satisfied 
with their result. 

(168.) This is the principle of the mural circle, which is 
nothing more than such a circle as we have described in art. 
163, firmly supported, in the plane of the meridian, on a 
long and powerful horizontal axis. This axis is let into 
a massive pier, or wall, of stone (whence the name of the 
instrument), and so secured by screws as to be capable of 
adjustment both in a vertical and horizontal direction; so 
that, like the axis of the transit, it can be maintained in the 
exact direction of the east and west points of the horizon, 
the plane of the circle being consequently truly meridional. 

(169.) The meridian, being at right angles to all the 
diurnal circles described by the stars, its arc intercepted 
between any two of them will measure the least distance be- 
tween these circles, and will be equal to the difference of 
the declinations, as also to the difference of the meridian 
altitudes of the objects — at least when corrected for refrac- 
tion. These differences, then, are the angular intervals 
directly measured by the mural circle. But from these, 
supposing the law and amount of refraction known, it is 
easy to conclude, not their differences only, but the quan- 
tities themselves, as we shall now explain. 

(170.) The declination of a heavenly body is the com- 



OUTLINES OF ASTRONOMY 141 

plement of its distance from the pole. The pole, being a 
point in the meridian, might be directly observed on the 
limb of the circle, if any star stood exactly therein; and 
thence the polar distances, and, of course, the declinations 
of all the rest might be at once determined. But this not 
being the case, a bright star as near the pole as can be 
found is selected, and observed in its upper and lower 
culminations; that is, when it passes the meridian above 
and below the pole. Now, as its distance from the pole 
remains the same, the difference of reading off the circle in 
the two cases is, of course (when corrected for refraction), 
equal to twice the polar distance 
of the star ; the arc intercepted on 
the limb of the circle being, in 
this case, equal to the angular 
diameter of the star' s diurnal cir- 
cle. In the annexed diagram, 
H P represents the celestial 
meridian, P the pole, BE, A Q, 
C B the diurnal circles of stars which arrive on the merid- 
ian at B, A, and C in their upper and at K, Q, B in their 
lower culminations, of which D and Q happen above the 
horizon HO. P is the pole ; and if we suppose h p o to 
be the mural circle, having S for its centre, b a cp d will 
be the points on its circumference corresponding to B A 
P D in the heavens. Now the arcs b a, b c, b d, and c d 
are given immediately by observation; and since C P= 
P D, we have also c p= p d, and each of them=i c d, con- 
sequently the place of the polar point, as it is called, upon 
the limb of the circle becomes known, and the arcs p b, p a, 
p c, which represent on the circle the polar distances re- 
quired, become also known. 




142 OUTLINES OF ASTRONOMY 

(171.) The situation of the pole star, which is a very 
brilliant one, is eminently favorable for this purpose, being 
only about a degree and half from the pole; it is, therefore, 
the star usually and almost solely chosen for this important 
purpose; the more especially because, both its culminations 
taking place at great and not very different altitudes, the 
refractions by which they are affected are of small amount, 
and differ but slightly from each other, so that their correc- 
tion is easily and safely applied. The brightness of the 
pole star, too, allows it to be easily observed in the daytime. 
In consequence of these peculiarities, this star is one of con- 
stant resort with astronomers for the adjustment and verifi- 
cation of instruments of almost every description. In the 
case of the transit, for instance, it furnishes an excellent 
object for the application of the method of testing the 
meridional situation of the instrument described in art. 
162, in fact, the most advantageous of any for that pur- 
pose, owing to its being the most remote from the zenith, 
at its upper culmination, of all bright stars observable both 
above and below the pole. 

(172.) The place of the polar point on the limb of the 
mural circle once determined, becomes an origin, or zero 
point, from which the polar distances of all objects, referred 
to other points on the same limb, reckon. It matters not 
whether the actual commencement 0° of the graduations 
stands there, or not: since it is only by the differences of the 
readings that the arcs on the limb are determined; and 
hence a great advantage is obtained in the power of com- 
mencing anew a fresh series of observations, in which a 
different part of the circumference of the circle shall be 
employed, and different graduations brought into use, by 
which inequalities of division may be detected and neutral- 



OUTLINES OF ASTRONOMY 143 

ized. This is accomplished practically by detaching the 
telescope from its old bearings on the circle, and fixing 
it afresh, by screws or clamps, on a different part of the 
circumference. 

(173.) A point on the limb of the mural circle, not less 
important than the polar point, is the horizontal point, which, 
being once known, becomes in like manner an origin, or 
zero point, from which altitudes are reckoned. The prin- 
ciple of its determination is ultimately nearly the same 
with that of the polar point. As no star exists in the 
celestial horizon, the observer must seek to determine two 
points on the limb, the one of which shall be precisely 
as far below the horizontal point as the other is above it. 
For this purpose, a star is observed at its culmination on 
one night, by pointing the telescope directly to it, and the 
next, by pointing to the image of the same star reflected in 
the still, unruffled surface of a fluid at perfect rest. Mer- 
cury, as the most reflective fluid known, is generally chosen 
for that use. As the surface of a fluid at rest is necessarily 
horizontal, and as the angle of reflection, by the laws of 
optics, is equal to that of incidence, this image will be just 
as much depressed below the horizon as the star itself is 
above it (allowing for the difference of refraction at the 
moments of observation). The arc intercepted on the limb 
of the circle between the star and its reflected image thus 
consecutively observed, when corrected for refraction, is 
the double altitude of the star, and its point of bisection 
the horizontal point. The reflecting surface of a fluid so 
used for the determination of the altitudes of objects is 
called an artificial horizon.™ 

10 By a peculiar and delicate manipulation and management of the setting, 
bisection and reading off of the circle, aided by the use of a movable horizontal 



144 OUTLINES OF ASTRONOMY 

(174.) The mural circle is, in fact, at the same time, a 
transit instrument; and, if furnished with a proper system 
of vertical wires in the focus of its telescope, may be used 
as such. As the axis, however, is only supported at one 
end, it has not the strength and permanence necessary for 
the more delicate purposes of a transit; nor can it be veri- 
fied, as a transit may, by the reversal of the two ends of its 
axis, east for west. Nothing, however, prevents a divided 
circle being permanently fastened on the axis of a transit 
instrument, either near to one of its extremities, or close 
to the telescope, so as to revolve with it, the reading off 
being performed by one or more microscopes fixed on one 
of its piers. Such an instrument is called a transit circle, 
or a meridian circle, and serves for the simultaneous de- 
termination of the right ascensions and polar distances of 
objects observed with it; the time of transit being noted 
by the clock, and the circle being read off by the lateral 
microscopes. There is much advantage, when extensive 
catalogues of small stars have to be formed, in this simul- 
taneous determination of both their celestial co-ordinates: 
to which may be added the facility of applying to the 
meridian circle a telescope of any length and optical power. 
The construction of the mural circle renders this highly in- 
convenient, and indeed impracticable beyond very moderate 
limits. 

(175.) The determination of the horizontal point on the 
limb of an instrument is of such essential importance in 
astronomy, that the student should be made acquainted with 

micrometric wire in the focus of the object-glass, it is found practicable to observe 
a slow moving star (as the pole star) on one and the same night, both by reflec- 
tion and direct vision, sufficiently near to either culmination to give the horizon- 
tal point, without risking the change of refraction in twenty -four hours ; so that 
this source of error is thus completely eliminated. 



OUTLINES OF ASTRONOMY 145 

every means employed for this purpose. These are, the 
artificial horizon, the plumb-line, the level, and the colli- 
mator. The artificial horizon has been already explained. 
The plumb-line is a fine thread or wire, to which is sus- 
pended a weight, whose oscillations are impeded and quickly 
reduced to rest by plunging it in water. The direction ulti- 
mately assumed by such a line, admitting its perfect flexibil- 
ity, is that of gravity, or perpendicular to the surface of still 
water. Its application to the purposes of astronomy is, 
however, so delicate, and difiicult, and liable to error, 
unless extraordinary precautions are taken in its use, that 
it is at present almost universally abandoned, for the more 
convenient, and equally exact instrument the level. 

(176.) The level is a glass tube nearly filled with a liquid 
(sulphuric ether, or chloroform, being those now generally 
used, on account of their extreme mobility, and not being 
liable to freeze), the bubble in which, when the tube is 




placed horizontally, would rest indifferently in any part if 
the tube could be mathematically straight. But that being 
impossible to execute, and every tube having some slight 
curvature ; if the convex side be placed upward the bubble 
will occupy the higher part, as in the figure (where the cur- 
vature is purposely exaggerated). Suppose such a tube, as 
A B, firmly fastened on a straight bar, C D, and marked at 
a b, two points distant by the length of the bubble; then, if 
the instrument be so placed that the bubble shall occupy 
Astronomy — Vol. XIX. — 7 



146 OUTLINES OF ASTRONOMY 

this interval, it is clear that C D can have no other than one 
definite inclination to the horizon ; because, were it ever so 
little moved one way or other, the bubble would shift its 
place, and run toward the elevated side. Suppose, now, 
that we would ascertain whether any given line P Q be hori- 
zontal; let the base of the level C D be set upon it, and note 
the points a 5, between which the bubble is exactly con- 
tained ; then turn the level end for end, so that G shall rest 
on Q, and D on P. If then the bubble continue to occupy 
the same place between a and b y it is evident that P Q can 
be no otherwise than horizontal. If not, the side toward 
which the bubble runs is highest, and must be lowered. 
Astronomical levels are furnished with a divided scale, by 
which the places of the ends of the bubble can be nicely 
marked; and it is said that they can be executed with such 
delicacy, as to indicate a single second of angular deviation 
from exact horizontality. In such levels accident is not 
trusted to to give the requisite curvature. They are ground 
and polished internally by peculiar mechanical processes of 
great delicacy. 

(177.) The mode in which a level may be applied to find 
the horizontal point on the limb of a vertical divided circle 
may be thus explained: Let A B be a telescope firmly fixed 
to such a circle, D EF, and movable in one with it on a 
horizontal axis C, which must be like that of a transit, sus- 
ceptible of reversal (see art. 161), and with which the circle 
is inseparably connected. Direct the telescope on some dis- 
tant wBll-defined object S, and bisect it by its horizontal 
wire, and in this position clamp it fast. Let L be a level 
fastened at right angles to an arm, L E F, furnished with a 
microscope, or vernier at F, and, if we please, another at E. 
Let this arm be fitted by grinding on the axis C, but capable 



OUTLINES OF ASTRONOMY 



147 



of moving smoothly on it without carrying it round, and 
also of being clamped fast on it, so as to prevent it from 
moving until required. While the telescope is kept fixed 
on the object S, let the level be set so as to bring its bubble 
to the marks a b, and clamp it there. Then will the arm 
L C F have some certain determinate inclination (no matter 
what) to the horizon. In this position let the circle be read 
off at F, and then let the whole apparatus be reversed by 
turning its horizontal axis end for end, without unclamping 
the level arm from the axis. This done, by the motion of 
the whole instrument (level and all) on its axis, restore the 
level to its horizontal position with 
the bubble at a b. Then we are 
sure that the telescope has now 
the same inclination to the hori- 
zon the other way, that it had when 
pointed to S, and the reading off 
at F will not have been changed. 
Now unclamp the level, and, 
keeping it nearly horizontal, turn 
round the circle on the axis, so 
as to carry back the telescope through the zenith to S, and 
in that position clamp the circle and telescope fast. Then 
it is evident that an angle equal to twice the zenith dis- 
tance of S has been moved over by the axis of the tele- 
scope from its last position. Lastly, without unclamping 
the telescope and circle, let the level be once more recti- 
fied. Then will the arm L E F once more assume the 
same definite position with respect to the horizon: and, 
consequently, if the circle be again read off, the differ- 
ence between this and the previous reading must measure 
the arc of its circumference which has passed under the 




148 OUTLINES OF ASTRONOMY 

point F, which may be considered as having all the while 
retained an invariable position. This difference, then, will 
be the double zenith distance of S, and its half will be the 
zenith distance simply, the complement of which is its alti- 
tude. Thus the altitude corresponding to a given reading 
of the limb becomes known, or, in other words, the hori- 
zontal point on the limb is ascertained. Circuitous as this 
process may appear, there is no other mode of employing 
the level for this purpose which does not in the end come to 
the same thing. Most commonly, however, the level is used 
as a mere fiducial reference, to preserve a horizontal point 
once well determined by other means, which is done by ad- 
justing it so as to stand level when the telescope is truly 
horizontal, and thus leaving it, depending on the perma- 
nence of its adjustment. 

(178.) The last, but probably not the least exact, as it 
certainly is, in innumerable cases, the most convenient 
means of ascertaining the horizontal point, is that afforded 
by the floating collimator, an invention of Captain Kater, 
but of which the optical principle was first employed by Kit- 
tenhouse, in 1785, for the purpose of fixing a definite direc- 



tion in space by the emergence of parallel rays from a mate- 
rial object placed in the focus of a fixed lens. This elegant 
instrument is nothing more than a small telescope furnished 
with a cross-wire in its focus, and fastened horizontally, or 
as nearly so as may be, on a flat iron float, which is made to 
swim on mercury, and which, of course, will, when left to 



OUTLINES OF ASTRONOMY 149 

itself, assume always one and the same invariable inclina- 
tion to the horizon. If the cross- wires of the collimator be 
illuminated by a lamp, being in the focus of its object-glass, 
the rays from them will issue parallel, and will therefore be 
in a fit state to be brought to a foe as by the object-glass of 
any other telescope, in which they will form an image as if 
they came from a celestial object in their direction, i,e. at an 
altitude equal to their inclination. Thus the intersection of 
the cross of the collimator may be observed as if it were a 
star, and that, however near the two telescopes are to each 
other. By transferring then, the collimator still floating on 
a vessel of mercury from the one side to the other of a cir- 
cle, we are furnished with two quasi- celestial objects, at pre- 
cisely equal altitudes, on opposite sides of the centre; and 
if these be observed in succession with the telescope of the 
circle, bringing its cross to bisect the image of the cross of 
the collimator (for which end the wires of the latter cross 
are purposely set 45° inclined to the horizon), the difference 
of the readings on its limb will be twice the zenith distance 
of either; whence, as in the last article, the horizontal or 
zenith point is immediately determined. Another, and, in 
many respects, preferable form of the floating collimator, in 
which the telescope is vertical, and whereby the zenith point 
is directly ascertained, is described in the Phil. Trans. 1828, 
p. 257, by the same author. 

(179.) By far the neatest and most delicate application of 
the principle of collimation of Eittenhouse, however, is sug- 
gested by Bohnenberger, which affords at once, and by a 
single observation, an exact knowledge of the nadir point 
of an astronomical circle. In this combination, the tele- 
scope of the circle is its own collimator. The object ob- 
served is the central intersectional cross of the wires in its 



150 



OUTLINES OF ASTRONOMY 



own focus reflected in mercury. A strong illumination 
being thrown upon the system of wires (art. 160) by a lateral 
lamp, the telescope of the instrument is directed vertically 

downward toward the surface of the 
mercury, as in the figure annexed. 
The rays diverging from the wires 
issue in parallel pencils from the 
object-glass, are incident on the 
mercury, and are thence reflected 
back (without losing their parallel 
character) to the object-glass, which 
is therefore enabled to collect them 
again in its focus. Thus is formed 
a reflected image of the system of 
cross- wires, which, when brought 
by the slow motion of the telescope 
to exact coincidence (intersection 
upon intersection) with the real system as seen in the eye- 
piece of the instrument, indicates the precise and rigorous 
vertically of the optical axis of the telescope when directed 
to the nadir point. 

(180.) The transit and mural circle are essentially merid- 
ian instruments, being used only to observe the stars at 
the moment of their meridian passage. Independent of this 
being the most favorable moment for seeing them, it is that 
in which their diurnal motion is parallel to the horizon. It 
is therefore easier at this time than it could be at any other, 
to place the telescope exactly in their true direction ; since 
their apparent course in the field of view being parallel to 
the horizontal thread of the system of wires therein, they 
may, by giving a fine motion to the telescope, be brought to 
exact coincidence with it, and time may be allowed to ex- 




****** 



OUTLINES OF ASTRONOMY 151 

amine and correct this coincidence, if not at first accurately 
hit, which is the case in no other situation. Generally 
speaking, all angular magnitudes which it is of importance 
to ascertain exactly, should, if possible, be observed at their 
maxima or minima of increase or diminution; because at 
these points they remain not perceptibly changed during a 
time long enough to complete, and even, in many cases, to 
repeat and verify, our observations in a careful and leisurely 
manner. The angle which, in the case before us, is in this 
predicament, is the altitude of the star, which attains its 
maximum or minimum on the meridian, and which is meas- 
ured on the limb of the mural circle. 

(181.) The purposes of astronomy, however, require that 
an observer should possess the means of observing any ob- 
ject not directly on the meridian, but at any point of its 
diurnal course, or wherever it may present itself in the 
heavens. Now, a point in the sphere is determined by 
reference to two great circles at right angles to each other; 
or of two circles, one of which passes through the pole of 
the other. These, in the language of geometry, are co-ordi- 
nates by which its situation is ascertained: for instance — on 
the earth, a place is known if we know its longitude and 
latitude ; — in the starry heavens, if we know its right ascen- 
sion and declination ; — in the visible hemisphere, if we know 
its azimuth and altitude, etc. 

(182.) To observe an object at any point of its diurnal 
course, we must possess the means of directing a telescope 
to it; which, therefore, must be capable of motion in two 
planes at right angles to each other; and the amount of its 
angular motion in each must be measured on two circles 
co-ordinate to each other, whose planes must be parallel to 
those in which the telescope moves. The practical accom- 



152 



OUTLINES OF ASTRONOMY 



plishment of this condition is effected by making the axis 
of one of the circles penetrate that of the other at right 
angles. The pierced axis turns on fixed supports, while the 
other has no connection with any external support, but is 
sustained entirely by that which it penetrates, which is 
strengthened and enlarged at the point of penetration to 
receive it. The annexed figure exhibits the simplest form 
of such a combination, though very far indeed from the best 
in point of mechanism. The two circles are read off by ver- 
niers, or microscopes; the one attached to the fixed support 
which carries the principal axis, the other to an arm project- 
ing from that axis. Both circles also are susceptible of 
being clamped, the clamps being attached to the same ulti- 
mate bearing with which the apparatus for reading off is 
connected. 

(183.) It is manifest that such a combination, however its 
principal axis be pointed (provided that its direction be in- 
variable), will enable us to ascertain 
the situation of any object with re- 
spect to the observer's station, by 
angles reckoned upon two great cir- 
cles in the visible hemisphere, one 
of which has for its poles the pro- 
longations of the principal axis or 
the vanishing points of a system of 
lines parallel to it, and the other 
passes always through these poles: 
for the former great circle is the 
vanishing line of all planes parallel 
to the circle A B, while the latter, in any position of the 
instrument, is the vanishing line of all the planes parallel 
to the circle Gr H ; and these two planes being, by the con- 




OUTLINES OF ASTRONOMY 153 

struction of the instrument, at right angles, the great circles, 
which are their vanishing lines, must be so too. Now, if 
two great circles of a sphere be at right angles to each other, 
the one will always pass through the other's poles. 

(184.) There are, however, but two positions in which 
such an apparatus can be mounted so as to be of any prac- 
tical utility in astronomy. The first is, when the principal 
axis C D is parallel to the earth's axis, and therefore points 
to the poles of the heavens which are the vanishing points 
of all lines in this system of parallels; and when, of course, 
the plane of the circle A B is parallel to the earth's equator, 
and therefore has the equinoctial for its vanishing circle, 
and measures, by its arcs read off, hour angles, or differ- 
ences of right ascension. In this case, the great circles in 
the heavens, corresponding to the various positions, which 
the circle Gr H can be made to assume, by the rotation of 
the instrument round its axis C D, are all hour-circles; and 
the arcs read off on this circle will be declinations, or polar 
distances, or their differences. 

(185.) In this position the apparatus assumes the name 
of an equatorial, or, as it was formerly called, a parallactic 
instrument. It is a most convenient instrument for all such 
observations as require an object to be kept long in view, 
because, being once set upon the object, it can be followed 
as long as we please by a single motion, i.e. by merely turn- 
ing the whole apparatus round on its polar axis. For since, 
when the telescope is set on a star, the angle between its 
direction and that of the polar axis is equal to the polar dis- 
tance of the star, it follows, that when turned about its axis, 
without altering the position of the telescope on the circle 
G H, the point to which it is directed will always lie in the 
small circle of the heavens coincident with the star's diurnal 



154 OUTLINES OF ASTRONOMY 

path. In many observations this is an inestimable advan- 
tage, and one which belongs to no other instrument. The 
equatorial is also used for determining the place of an un- 
known by comparison with that of a known object/ in a 
manner to be described in the fifth chapter. The adjust- 
ments of the equatorial are somewhat complicated and diffi- 
cult. They are best performed in this manner: — 1st, Follow 
the pole star round its whole diurnal course, by which it 
will become evident whether the polar axis is directed 
above or below, to the right or to the left, of the true pole 
— and correct it accordingly (without any attempt, during 
this process, to correct the errors, if any, in the position of 
the declination axis). 2dly, after the polar axis is thus 
brought into adjustment, place the plane of the declination 
circle in or near the meridian; and, having there secured it, 
observe the transits of several known stars of widely differ- 
ent declinations. If the intervals between these transits 
correspond to the known differences of right ascensions of 
the stars, we may be sure that the telescope describes a true 
meridian, and that, therefore, the declination axis is truly 
perpendicular to the polar one; — if not, the deviation of 
the intervals from this law will indicate the direction and 
amount of the deviation of the axis in question, and enable 
us to correct it." 

(186.) A very great improvement has, within a few years 
from the present time, been introduced into the construc- 
tion of the equatorial instrument. It consists in applying 
a clock-work movement to turn the whole instrument round 



11 See Littrow on the Adjustment of the Equatorial (Mem. Ast. Soc. vol. ii. 
p. 45), where formulae are given for ascertaining the amount and direction of all 
the misadjustments simultaneously. But the practical observer, who wishes 
to avoid bewildering himself by doing two things at once, had better proceed 
as recommended in the text. 



OUTLINES OF ASTRONOMY 155 

"upon its polar axis, and so to follow the diurnal motion of 
any celestial object, without the necessity of the observer's 
manual intervention. The driving power is the descent of 
a weight which communicates motion to a train of wheel- 
work, and thus, ultimately, to the polar axis, while, at the 
same time, its too swift descent is controlled and regulated 
to the exact and uniform rate required to give that axis one 
turn in 24 hours, by connecting it with a regulating clock, 
or (which is found preferable in practice) by exhausting all 
the superfluous energy of the driving power, by causing 
it to overcome a regulated friction. Artists have thus suc- 
ceeded in obtaining a perfectly smooth, uniform, and regu- 
lable motion, which, when so applied, serves to retain any 
object on which the telescope may be set, commodiously, 
in the centre of the field of view for whole hours in succes- 
sion, leaving the attention of the observer undistracted by 
having a mechanical movement to direct ; and with both his 
hands at liberty. 

(187.) The other position in which such a compound 
apparatus as we have described in art. 182 may be advan- 
tageously mounted, is that in which the principal axis 
occupies a vertical position, and the one circle, A B, con- 
sequently corresponds to the celestial horizon, and the 
other, Gr H, to a vertical circle of the heavens. The angles 
measured on the former are therefore azimuths, or differ- 
ences of azimuth, and those of the latter zenith distances, 
or altitudes, according as the graduation commences from 
the upper point of its limb, or from one 90° distant from it. 
It is therefore known by the name of an azimuth and alti- 
tude instrument. The vertical position of its principal axis 
is secured either by a plumb-line suspended from the upper 
end, which, however it be turned round, should continue 



156 OUTLINES OF ASTRONOMY 

always to intersect one and the same fiducial mark near its 
lower extremity, or by a level fixed directly across it, whose 
bubble ought not to shift its place, on moving the instru- 
ment in azimuth. The north or south point on the hori- 
zontal circle is ascertained by bringing the vertical circle 
to coincide with the plane of the meridian, by the same 
criterion by which the azimathal adjustment of the transit 
is performed (art. 162), and noting, in this position, the 
reading off of the lower circle; or by the following process. 
(188.) Let a bright star be observed at a considerable 
distance to the east of the meridian, by bringing it on the 
cross wires of the telescope. In this position let the hori- 
zontal circle be read off, and the telescope securely clamped 
on the vertical one. When the star has passed the merid- 
ian, and is in the descending point of its daily course, let 
it be followed by moving the whole instrument round to the 
west, without, however, unclamping the telescope, until 
it comes into the field of view; and until, by continuing 
the horizontal motion, the star and the cross of the wires 
come once more to coincide. In this position it is evident 
the star must have the same precise altitude above the 
western horizon, that it had at the moment of the first 
observation above the eastern. At this point let the motion 
be arrested, and the horizontal circle be again read off. 
The difference of the readings will be the azimuthal arc 
described in the interval. Now, it is evident that when 
the altitudes of any star are equal on either side of the 
meridian, its azimuths, whether reckoned both from the 
north or both from the south point of the horizon, must 
also be equal — consequently the north or south point of the 
horizon must bisect the azimuthal arc thus determined, and 
will therefore become known. 



OUTLINES OF ASTRONOMY 157 

(189.) This method of determining the north and south 
points of a horizontal circle is called the "method of equal 
altitudes/' and is of great and constant use in practical 
astronomy. If we note, at the moments of the two obser- 
vations, the time, by a clock or chronometer, the instant 
halfway between them will be the moment of the star's 
meridian passage, which may thus be determined without 
a transit; and, vice versa, the error of a clock or chronom- 
eter may by this process be discovered. For this last 
purpose, it is not necessary that our instrument should be 
provided with a horizontal circle at all. Any means by 
which altitudes can be measured will enable us to deter- 
mine the moments when the same star arrives at equal alti- 
tudes in the eastern and western halves of its diurnal course ; 
and, these once known, the instant of meridian passage and 
the error of the clock become also known. 

(190.) Thus also a meridian line may be drawn and a 
meridian mark erected. For the readings of the north and 
south points on the limb of the horizontal circle being 
known, the vertical circle may be brought exactly into the 
plane of the meridian, by setting it to that precise reading. 
This done, let the telescope be depressed to the north hori- 
zon, and let the point intersected there by its cross-wires 
be noted, and a mark erected there, and let the same be 
done for the south horizon. The line joining these points 
is a meridian line, passing through the centre of the hori- 
zontal circle. The marks may be made secure and perma- 
nent if required. 

(191.) One of the chief purposes to which the altitude 
and azimuth circle is applicable is the investigation of the 
amount and laws of refraction. For, by following with it 
a circumpolar star which passes the zenith, and another 



158 OUTLINES OF ASTRONOMY 

which grazes the horizon, through their whole diurnal 
course, the exact apparent form of their diurnal orbits, or 
the ovals into which their circles are distorted by refraction, 
can be traced; and their deviation from circles, being at 
every moment given by the nature of the observation in the 
direction in which the refraction itself takes place (i.e. in alti- 
tude), is made a matter of direct observation. 

(192.) The zenith sector and the theodolite are peculiar 
modifications of the altitude and. azimuth instrument. The 
former is adapted for the very exact observation of stars in 
or near the zenith, by giving a great length to the vertical 
axis, and suppressing all the circumference of the vertical 
circle, except a few degrees of its lower part, by which 
a great length of radius, and a consequent proportional 
enlargement of the divisions of its arc, is obtained. The 
latter is especially devoted to the measures of horizontal 
angles between terrestrial objects, in which the telescope 
never requires to be elevated more than a few degrees, and 
in which, therefore, the vertical circle is either dispensed 
with, or executed on a smaller scale, and with less delicacy ; 
while, on the other hand, great care is bestowed on securing 
the exact perpendicularity of the plane of the telescope's 
motion, by resting its horizontal axis on two supports like 
the piers of a transit instrument, which themselves are firmly 
bedded on the spokes of the horizontal circle, and turn 
with it. 

(193.) The next instrument we shall describe is one by 
whose aid the angular distance of any two objects may be 
measured, or the altitude of a single one determined, either 
by measuring its distance from the visible horizon (such as 
the sea- offing, allowing for its dip), or from its own reflec- 
tion on the surface of mercury. It is the sextant, or quad- 



OUTLINES OF ASTRONOMY 159 

rant, commonly called Hadley's, from its reputed inventor, 
though the priority of invention belongs undoubtedly to 
Newton, whose claims to the gratitude of the navigator 
are thus doubled, by his having furnished at once the only 
theory by which his vessel can be securely guided, and the 
only instrument which has ever been found to avail, in 
applying that theory to its nautical uses. 13 

(194.) The principle of this instrument is the optical 
property of reflected rays, thus announced: "The angle 
between the first and last directions of a ray which has 
suffered two reflections in one plane is equal to twice the 
inclination of the reflecting surfaces to each other." Let 
A B be the limb, or graduated arc, of a portion of a circle 
60° in extent, but divided into 120 equal parts. On the 
radius C B let a silvered plane glass D be fixed, at right 
angles to the plane of the circle, and on the movable radius 
C E let another such silvered glass, C, be fixed. The glass 
D is permanently fixed parallel to A C, and only one half 
of it is silvered, the other half allowing objects to be seen 
through it. The glass C is wholly silvered, and its plane 
is parallel to the length of the movable radius C E, at the 
extremity E of which a vernier is placed to read off the 
divisions of the limb. On the radius A C is set a telescope 
F, through which any object, Q, may be seen by direct rays 
which pass through the unsilvered portion of the glass D, 
while another object, P, is seen through the same telescope 
by rays, which, after reflection at C, have been thrown upon 



H Newton communicated it to Dr. Halley, who suppressed it. The descrip- 
tion of the instrument was found, after the death of Halley, among his papers, 
in Newton's own handwriting, by his executor, who communicated the papers 
to the Royal Society, twenty-five years after Newton's death, and eleven after 
the publication of Hadley's invention, which might be, and probably was, inde- 
pendent of any knowledge of Newton's, though Hutton insinuates the contrary. 




160 OUTLINES OF ASTRONOMY 

the silvered part of D, and are thence directed by a second 
reflection into the telescope. The two images so formed 
will both be seen in the field of view at once, and by 
moving the radius C E will (if the reflectors be truly per- 
pendicular to the plane of the circle) meet and pass over, 

without obliterating each other. 
The motion, however, is arrested 
when they meet, and at this point 
the angle included between the 
direction C P of one object, and 
F Q of the other, is twice the an- 
gle E C A included between the 
fixed and movable radii C A, C E. 
Now, the graduations of the limb being purposely made 
only half as distant as would correspond to degrees, the 
arc A E, when read off, as if the graduations were whole de- 
grees, will, in fact, read double its real amount, and there- 
fore the numbers so read off will express not the angle 
EGA, but its double, the angle subtended by the objects. 
(195.) To determine the exact distances between the stars 
by direct observation is comparatively of little service; but 
in nautical astronomy the measurement of their distances 
from the moon, and of their altitudes, is of essential impor- 
tance; and as the sextant requires no fixed support, but 
can be held in the hand, and used on shipboard, the utility 
of the instrument becomes at once obvious. For altitudes 
at sea, as no level, plumb-line, or artificial horizon can be 
used, the sea-offing affords the only resource; and the image 
of the star observed, seen by reflection, is brought to co- 
incide with the boundary of the sea seen by direct rays. 
Thus the altitude above the sea-line is found; and this 
corrected for the dip of the horizon (art. 23) gives the true 



OUTLINES OF ASTRONOMY 161 

altitude of the star. On land, an artificial horizon may be 
used (art. 173), and the consideration of dip is rendered 
unnecessary. 

(196.) The adjustments of the sextant are simple. They 
consist in fixing the two reflectors, the one on the revolving 
radius C E, the other on the fixed one C B, so as to have 
their planes perpendicular to the plane of the circle, and 
parallel to each other, when the reading of the instrument 
is zero. This adjustment in the latter respect is of little 
moment, as its effect is to produce a constant error, whose 
amount is readily ascertained by bringing the two images 
of one and the same star or other distant object to coinci- 
dence; when the instrument ought to read zero, and if it 
does not, the angle which it does read is the zero correction 
and must be subtracted from all angles measured with the 
sextant. The former adjustments are essential to be main- 
tained, and are performed by small screws, by whose aid 
either or both the glasses may be tilted a little one way or 
another until the direct and reflected images of a vertical 
line (a plumb-line) can be brought to coincidence over their 
whole extent, so as to form a single unbroken straight line, 
whatever be the position of the movable arm, in the middle 
of the field of view of the telescope, whose axis is carefully 
adjusted by the optician to parallelism with the plane of the 
limb. In practice it is usual to leave only the reflector D 
on the fixed radius adjustable, that on the movable being 
set to great nicety by the maker. In this case the best way 
of making the adjustment is to view a pair of lines crossing 
each other at right angles (one being horizontal, the other 
vertical) through the telescope of the instrument, holding 
the plane of its limb vertical — then having brought the 
horizontal line and its reflected image to coincidence by 



162 OUTLINES OF ASTRONOMY 

the motion of the radius, the two images of the vertical 
arm must be brought to coincidence by tilting one way or 
other the fixed reflector D by means of an adjusting screw, 
with which every sextant is provided for that purpose. 
When both lines coincide in the centre of the field the ad- 
justment is correct. 

(197.) The reflecting circle is an instrument destined for 
the same uses as the sextant, but more complete, the circle 
being entire, and the divisions carried all round. It is 
usually furnished with three verniers, so as to admit of 
three distinct readings off, by the average of which the 
error of graduation and of reading is reduced. This is alto- 
gether a very refined and elegant instrument. 

(198.) We must not conclude this part of our subject 
without mention of the "principle of repetition"; an inven- 
tion of Borda, by which the error of graduation may be 
diminished to any degree, and, practically speaking, anni- 
hilated. Let P Q be two objects which we may suppose 
fixed, for purposes of mere explanation, and let K L be 
a telescope movable on 0, the common axis of two circles, 
AML and a b c, of which the former, A M L, is absolutely 
fixed in the plane of the objects, and carries the graduations, 
and the latter is freely movable on the axis. The telescope 
is attached permanently to the latter circle, and moves with 
it. An arm O a A carries the index, or vernier, which 
reads off the graduated limb of the fixed circle. This arm 
is provided with two clamps, by which it can be temporarily 
connected with either circle, and detached at pleasure. 
Suppose, now, the telescope directed to P. Clamp the 
index arm O A to the inner circle, and unclamp it from 
the outer, and read off. Then carry the telescope round to 
the other object Q. In so doing, the inner circle, and the 



OUTLINES OF ASTRONOMY 163 

index-arm which is clamped to it, will also be carried round, 
over an arc A B, on the graduated limb of the outer, equal 
to the angle P Q. Now clamp the index to the outer 
circle, and unclamp the inner, and read off: the difference 
of readings will of course measure the angle P O Q; but 
the result will be liable to two sources of error — that of 
graduation and that of observation, both which it is our 
object to get rid of. To this end transfer the telescope 
back to P, without unclamping the arm from the outer 
circle; then, having made the bisection of P, clamp the 
arm to b, and unclamp it from B, and 
again transfer the telescope to Q, by 
which the arm will now be carried 
with it to C, over a second arc, B 
C, equal to the angle P O Q. Now 
again read off; then will the differ- 
ence between this reading and the 
original one measure twice the angle 
P O Q, affected with both errors 
of observation, but only with the 

same error of graduation as before. Let this process be re- 
peated as often as we please (suppose ten times) ; then will 
the final arc ABCD read off on the circle be ten times the 
required angle, affected by the joint errors of all the ten 
observations, but only by the same constant error of gradua- 
tion, which depends on the initial and final readings off 
alone. Now the errors of observation, when numerous, 
tend to balance and destroy one another; so that, if suffi- 
ciently multiplied, their influence will disappear from the 
result. There remains, then, only the constant error of 
graduation, which comes to be divided in the final result 
by the number of observations, and is therefore diminished 




164 



OUTLINES OF ASTRONOMY 



in its influence to one- tenth of its possible amount, or to 
less if need be. The abstract beauty and advantage of this 
principle seem to be counterbalanced in practice by some 
unknown cause, which, probably, must be sought for in 
imperfect clamping. 

(199.) Micrometers are instruments (as the name im- 
ports 13 ) for measuring, with great precision, small angles, 
not exceeding a few minutes, or at most a whole degree. 
They are very various in construction and principle, nearly 
all, however, depending on the exceeding delicacy with 
which space can be subdivided by the turns and parts of 
a turn of fine screws. Thus — in the parallel wire microm- 
eter, two parallel threads (spider's lines are generally 
used) stretched on sliding frames, one or both movable by 




screws in a direction perpendicular to that of the threads, 
are placed in the common focus of the object and eye- 
glasses of a telescope, and brought by the motion of the 
screws exactly to cover the two extremities of the image 
of any small object seen in the telescope, as the diameter 
of a planet, etc., the angular distance between which it is 
required to measure. This done, the threads are closed 
up by turning one of the screws till they exactly cover 
each other, and the number of turns and parts of a turn 



Mi/cpos, small ; /nerpeiv, to measure. 



OUTLINES OF ASTRONOMY 165 

required gives the interval of the threads, which must be 
converted into angular measure, either by actual calculation 
from the linear measure of the threads of the screw and the 
focal length of the object-glass, or experimentally, by meas- 
uring the image of a known object placed at a known dis- 
tance (as a foot-rule at a hundred yards, etc.) and therefore 
subtending a known angle. 

(200.) The duplication of the image of an object by optical 
means furnishes a valuable and fertile resource in microme- 
try. Suppose by any optical contrivance the single image 
A of any object can be converted into two, exactly equal 
and similar, A B, at a distance from one another, dependent 
(by some mechanical movement) on the will of the observer, 
and in any required direction from one another. As these 





can, therefore, be made to approach to or recede from each 
other at pleasure, they may be brought in the first place to 
approach till they touch one another on one side, as at A C, 
and then being made by continuing the motion to cross and 
touch on the opposite side, as A D, it is evident that the 
quantity of movement required to produce the change from 
one contact to the other, .if uniform, will measure the double 
diameter of the object A. 

(201.) Innumerable optical combinations may be devised 
to operate such duplication. The chief and most important 
(from its recent applications), is the heliometer, in which the 
image is divided by bisecting the object-glass of the telescope, 
and making its two halves, set in separate brass frames, 




166 OUTLINES OF ASTRONOMY 

slide laterally on each other, as A B, the motion being 
produced and measured by a screw. Each half, by the 

laws of optics, forms its own 
image (somewhat blurred, it 
is true, by diffraction 14 ), in 
its own axis; and thus two 
equal and similar images are 
formed side by side in the 
focus of the eye-piece, which 
may be made to approach and 
recede by the motion of the screw, and thus afford the 
means of measurement as above described. 

(202.) Double refraction through crystallized media af- 
fords another means of accomplishing the same end. With- 
out going into the intricacies of this difficult branch of 
optics, it will suffice to state that objects viewed through 
certain crystals (as Iceland spar, or quartz) appear double, 
two images equally distinct being formed, whose angular 
distance from each other varies from nothing (or perfect 
coincidence), up to a certain limit, according to the direction 
with respect to a certain fixed line -in the crystal, called its 
optical axis. Suppose, then, to take the simplest case, that 
the eye-lens of a telescope, instead of glass, were formed of 
such a crystal (say of quartz, which may be worked as well 
or better than glass), and of a spherical form, so as to offer 
no difference when turned about on its centre, other than 
the inclination of its optical axis to the visual ray. Then 
when that axis coincides with the line of collimation of the 
object-glass, one image only will be seen, but when made to 
revolve on an axis perpendicular to that line, two will arise, 

14 This might be cured, though at an expense of light, by limiting each half 
to a circular space by diaphragms, as represented by the dotted lines. 



OUTLINES OF ASTRONOMY 167 

opening gradually out from each other, and thus originating 
the desired duplication. In this contrivance, the angular 
amount of the rotation of the sphere affords the necessary 
datum for determining the separation of the images. 

(203.) Of all methods which have been proposed, how- 
ever, the simplest and most unobjectionable would appear 
to be the following. It is well known to every optical stu- 
dent, that two prisms of glass, a flint and a crown, may be 
opposed to each other, so as to produce a colorless deflection 
of parallel rays. An object seen through such a compound 
or achromatic prism will be seen simply deviated in direc- 
tion, but in no way otherwise altered or distorted. Let 
such a prism be constructed with its surfaces so nearly 
parallel that the total deviation produced in traversing them 
shall not exceed a small amount 
(say 5'). Let this be cut in half, 
and from each half let a circular 
disk be formed, and cemented on 
a circular plate of parallel glass, 
or otherwise sustained, close to 
and concentric with the other by 
a framework of metal so light as 
to intercept but a small portion 
of the light which passes on the outside (as in the above 
figure), where the dotted lines represent the radii sustaining 
one, and the undotted those carrying the other disk. The 
whole must be so mounted as to allow one disk to revolve 
in its own plane behind the other, fixed, and to allow the 
amount of rotation to be read off. It is evident, then, that 
when the deviations produced by the two disks conspire, a 
total deviation of 10' will be effected on all the light which 
has passed through them; that when they oppose each 




168 OUTLINES OF ASTRONOMY 

other, the rays will emerge undeviated, and that in inter- 
mediate positions a deviation varying from to 10', and 
calculable from the angular rotation of the one disk on the 
other, will arise. Now, let this combination be applied at 
such a point of the cone of rays, between the object-glass 
and its focus, that the disks shall occupy exactly half the 
area of its section. Then will half the light of the object 
lens pass un deviated — the other half deviated, as above 
described; and thus a duplication of image, variable and 
measureable, (as required for micrometric measurement) will 
occur. If the object-glass be not very large, the most con- 
venient point of its application will be externally before it, 
in which case the diameter of the disks will be to that of the 
object-glass as 707 : 1000; or (allowing for the spokes) about 
as 7 to 10. 

(204. ) The Position Micrometer is simply a straight thread 
or wire, which is carried round by a smooth revolving mo- 
tion, in the common focus of the object and eye glasses, in a 
plane perpendicular to the axis of the telescope. It serves 
to determine the situation with respect to some fixed line 
in the field of view, of the line joining any two objects or 
points of an object seen in that field — as two stars, for in- 
stance, near enough to be seen at once. For this purpose 
the movable thread is placed so as to cover both of them, 
or stand, as may best be judged, parallel to their line of 
junction. And its angle, with the fixed one, is then read 
off upon a small divided circle exterior to the instrument. 
When such a micrometer is applied (as it most commonly 
is) to an equatorially mounted telescope, the zero of its po- 
sition corresponds to a direction of the wire, such as, pro- 
longed, will represent a circle of declination in the heavens 
— and the ' ' angles of position' ' so read off are reckoned in- 



OUTLINES OF ASTRONOMY 169 

variably from one point, and in one direction, viz., north, 
following, south, preceding] so that 0° position corresponds 
to the situation of an object exactly north of that assumed 
as a centre of reference — 90° to a situation exactly eastward, 
or following', 180° exactly south: and 270° exactly west, or 
preceding in the order of diurnal movement. When the 
relative position of two stars, very near to each other, so as 
to be seen at once in the same field of view, is to be deter- 
mined in this way, especially if they be of unequal magni- 
tudes, the best form of the instrument consists, not in a sin- 
gle thin wire to be placed centrally across both the stars, 
but in two thick parallel wires, between which both stars are 
brought under inspection in a symmetrical situation, by 
which arrangement the parallelism of the line joining their 
centres with the direction of the wires can be very much 
more accurately judged of. It gives great advantage, more- 
over, to the precision of such a judgment, if the position of 
the observer be such as to bring the principal section of his 
eye (that which in his upright position is vertical) into 
parallelism with the wires. 

(204 a.) To see the fiducial threads or wires of an eye- 
piece or micrometer in a dark night is impossible without 
introducing some artificial light into the telescope, so as 
either to illuminate the field of view, leaving the threads 
dark, or vice versd. To illuminate the field, the light of a 
lamp is introduced by a lateral opening into the tube of the 
telescope, and dispersed by reflection on a white unpolished 
surface, so arranged as not to intercept any part of the cone 
of rays going to form the image. For illuminating the 
wires, direct lamp light is thrown on them from the side 
toward the eye; the superfluous rays being stifled by falling 

on a black internal coating, or suffered to pass out to the 
Astronomy — Vol. XIX — 8 



170 OUTLINES OF ASTRONOMY 

tube through an opposite aperture opening into a dark 
chamber. 

(204 b.) When the wires are seen dark on an illuminated 
field, the color of the illuminating light is of great impor- 
tance. As a matter of experience, it is certain that a red 
illumination affords, a far sharper and clearer view of the 
wires than any other. 

(204 c.) For observing the sun, darkening glasses are 
necessary. In this case red glasses are inappropriate, be- 
cause they transmit the solar heat freely, by which the eye 
would be seriously injured, and even when very deep tinted, 
render prolonged inspection intolerably painful. Green 
glasses are free from this objection. The best darkening 
glass, however, is a combination of a cobalt blue with a 
green glass, which, if the components are properly selected, 
transmits an almost homogeneous yellow light, and no sen- 
sible amount of heat. Both the light and heat of the sun, 
however, may be subdued by reflection at glass surfaces, the 
light returned by regular reflection on glass being only 
about 2^ per cent of that incident on it. A reflecting tele- 
scope specifically adapted for viewing the sun may be con- 
structed by making the specula of glass, the object-mirror 
having the form of a double concave lens, whose anterior 
surface (that producing the image) is worked into a parab- 
oloid of the proper focal length, and the posterior to a 
sphere of considerably greater curvature to transmit and 
disperse outward the refracted rays into the open air behind 
(for which purpose the telescope should be open at both 
ends) and to so weaken those reflected by dispersing them 
as not to interfere with the distinctness of the image. 
Neither the quality of the glass, nor accuracy of figure in 
the posterior surface, is of any importance to the good per- 



OUTLINES OF ASTRONOMY 171 

formance of such, a reflector. 16 Should the light be not suffi- 
ciently enfeebled by the first reflection, it may be still fur- 
ther reduced (to about 1 — 900 th part of its original intensity) 
by making the small speculum of glass also in the form of a 
prism; the reflection being performed on one of its exterior 
surfaces, and the refracted portion being turned away and 
thrown out at the other. 

(204 d.) Advantage may be also taken (as in Sir D. 
Brewster's polarizing eye- piece) of the properties of polar- 
ized light, which may be diminished in any required degree 
by partial reflection in a plane at right angles to that of its 
first oblique reflection. Or without polarization, the light 
may be enfeebled by successive reflections between parallel 
surfaces to any extent. 

(204 e.) When the object in view is to scrutinize, under 
high magnifying powers, minute portions of the solar disk ; 
the light and heat of the general surface may be intercepted 
by a metallic screen placed in the focus where the image is 
formed, and pierced with a very small hole, allowing that 
minute portion only to pass through and be examined with 
the eye-piece; the observer being thus defended from the 
glare. By this arrangement, Mr. Dawes, to whom the idea 
is due, has been enabled to observe some very extraordi- 
nary peculiarities in the constitution of the sun's surface, 
discernible in no other way, an account of which will be 
found in their proper place. 

(204 /.) Since the use of large reflectors has become 
common among astronomers, the necessity of supporting 
the ponderous masses of their specula without constraint 



15 I would take this opportunity earnestly to recommend the construction of 
a helioscope on this principle, first propounded and more fully described in my 
Cape Observations (p. 436), to the attention of the practical optician. 



172 OUTLINES OF ASTRONOMY 

or undue pressure in any direction (which would distort the 
figure of their polished surfaces), renders the use of some 
ready method of verifying, from instant to instant, the 
adjustment of their lines of collimation (or the optical axis 
of the reflectors), and of readjusting it, when shifted, indis- 
pensable. For this purpose, a small collimating telescope 
(art. 178), illuminated by reflection from a lamp outside, is 
fixed within the tube of the reflector, its object- end being 
turned toward the speculum. Upon the image of the cross- 
wires of this telescope formed in the focus of the reflector, 
and seen through its eye-piece as a real object, the transits 
and altitudes of celestial objects may be observed as if it 
consisted of actual wires; for these, it is manifest, if once 
placed so as to bisect a star, will continue to do so, what- 
ever amount of tilting the reflector might be subjected to, 
either in a lateral or vertical plane. The rays from the star 
and the axis of the collimator remaining parallel, the latter 
axis, and not that of the reflector, becomes in fact the real 
line of collimation or optic axis of the instrument, when 
objects are thus directly referred to it. Should conven- 
ience of micrometric measurement, or the observation of 
faint objects in a very feebly illuminated field, preclude 
such direct reference, the position of the speculum must 
from time to time be examined, and if faulty, readjusted 
by bringing the micrometer wires to coincidence with the 
image of those of the collimator by an appropriate mechan- 
ism communicating the requisite small amount of movement 
to the speculum in its cell. 18 

16 See Phil. Trans. 1833, pp. 448-9, where this application of the collimating 
principle used by the author since 1833, is first described. See also "Results of 
Astronomical Observation at the Cape of G-ood Hope," preface, p. xiv. 



OUTLINES OF ASTRONOMY 173 



CHAPTER IV 

OF GEOGRAPHY 

Of the Figure of the Earth — Its Exact Dimensions — Its Form that of Equi- 
librium Modified by Centrifugal Force — Variation of Gravity on its 
Surface — Statical and Dynamical Measures of Gravity — The Pendulum 
— Gravity to a Spheroid — Other Effects of the Earth's Rotation — Trade 
Winds — Veering of the Winds — Cyclones — Foucault's Pendulum — The 
Gyroscope — Determination of Geographical Positions — Of Latitudes — 
Of Longitudes — Conduct of a Trigonometrical Survey — Of Maps — Pro- 
jections of the Sphere — Measurement of Heights by the Barometer 

(205.) Geography is not only the most important of 
the practical branches of knowledge to which astronomy 
is applied, but it is also, theoretically speaking, an essen- 
tial part of the latter science. The earth being the general 
station from which we view the heavens, a knowledge of 
the local situation of particular stations on its surface is of 
great consequence, when we come to inquire the distances 
of the nearer heavenly bodies from us, as concluded from 
observations of their parallax as well as on all other occa- 
sions, where a difference of locality can be supposed to 
influence astronomical results. "We propose, therefore, in 
this chapter, to explain the principles by which astronom- 
ical observation is applied to geographical determinations, 
and to give at the same time an outline of geography so far 
as it is to be considered a part of astronomy. 

(206.) G-eography, as the word imports, is a delineation 
or description of the earth. In its widest sense, this com- 
prehends not only the delineation of the form of its conti- 



174 OUTLINES OF ASTRONOMY 

nents and seas, its rivers and mountains, but their physical 
condition, climates, and products, and their appropriation 
by communities of men. With physical and political geog- 
raphy, however, we have no concern here. Astronomical 
geography has for its objects the exact knowledge of the 
form and dimensions of the earth, the parts of its surface 
occupied by sea and land, and the configuration of the sur- 
face of the latter, regarded as protuberant above the ocean, 
and broken into the various forms of mountain, tableland 
and valley; neither should the form of the bed of the ocean, 
regarded as a continuation of the surface of the land beneath 
the water, be left out of consideration: we know, it is true, 
very little of it; but this is an ignorance rather to be 
lamented, and, if possible, remedied, than acquiesced in, 
inasmuch as there are many very important branches 
of inquiry which would be greatly advanced by a better 
acquaintance with it. 

(207.) With regard to the figure of the earth as a whole, 
we have already shown that, speaking loosely, it may be 
regarded as spherical; but the reader who has duly appre- 
ciated the remarks in art. 22 will not be at a loss to perceive 
that this result, concluded from observations not susceptible 
of much exactness, and embracing very small portions of 
the surface at once, can only be regarded as a first approxi- 
mation, and may require to be materially modified by enter- 
ing into minutiae before neglected, or by increasing the 
delicacy of our observations, or by including in their ex- 
tent larger areas of its surface. For instance, if it should 
turn out (as it will), on minuter inquiry, that the true figure 
is somewhat elliptical, or flattened, in the manner of an 
orange, having the diameter which coincides with the axis 
about 3^o tn P art shorter than the diameter of its equatorial 



OUTLINES OF ASTRONOMY 175 

circle; — this is so trifling a deviation from the spherical 
form that, if a model of such proportions were turned in 
wood, and laid before us on a table, the nicest eye or hand 
would not detect the flattening, since the difference of diam- 
eters, in a globe of fifteen inches, would amount only to -g^th 
of an inch. In all common parlance, and for all ordinary 
purposes, then, it would still be called a globe; while, 
nevertheless, by careful measurement, the difference would 
not fail to be noticed; and, speaking strictly, it would be 
termed, not a globe, but an oblate ellipsoid, or spheroid, 
which is the name appropriated by geometers to the form 
above described. 

(208.) The sections of such a figure by a plane are not 
circles, but ellipses; so that, on such a shaped earth, the 
horizon of a spectator would nowhere (except at the poles) 
be exactly circular, but somewhat elliptical. It is easy to 
demonstrate, however, that its deviation from the circular 
form, arising from so very slight an ' ;l ellipticity^ as above 
supposed, would be quite imperceptible, not only to our 
eyesight, but to the test of the dip-sector; so that by that 
mode of observation we should never be led to notice so 
small a deviation from perfect sphericity. How we are led 
to this conclusion, as a practical result, will appear, when 
we have explained the means of determining with accuracy 
the dimensions of the whole, or any part of the earth. 

(209.) As we cannot grasp the earth, nor recede from 
it far enough to view it at once as a whole, and compare it 
with a known standard of measure in any degree commen- 
surate to its own size, but can only creep about upon it, 
and apply our diminutive measures to comparatively small 
parts of its vast surface in succession, it becomes necessary 
to supply, by geometrical reasoning, the defect of our phys- 



176 OUTLINES OF ASTRONOMY 

ical powers, and from a delicate and careful measurement 
of such small parts to conclude the form and dimensions 
of the whole mass. This would present little difficulty, if 
we were sure the earth were strictly a sphere, for the pro- 
portion of the circumference of a circle to its diameter being 
known (viz., that of 31415026 to 1-0000000), we have only 
to ascertain the length of the entire circumference of any 
great circle, such as a meridian, in miles, feet, or any other 
standard units, to know the diameter in units of the same 
kind. Now, the circumference of the whole circle is known 
as soon as we know the exact length of any aliquot part 
of it, such as 1° or -5^-0 th part; and this, being not more than 
about seventy miles in length, is not beyond the limits of 
very exact measurement, and could, in fact, be measured 
(if we knew its exact termination at each extremity) within 
a very few feet, or, indeed, inches, by methods presently 
to be particularized. 

(210.) Supposing, then, we were to begin measuring with 
all due nicety from any station, in the exact direction of a 
meridian, and go measuring on, till by some indication we 
were informed that we had accomplished an exact degree 
from the point we set out from, our problem would then 
be at once resolved. It only remains, therefore, to inquire 
by what indications we can be sure, 1st, that we have ad- 
vanced an exact degree; and, 2dly, that we have been 
measuring in the exact direction of a great circle. 

(211.) Now, the earth has no landmarks on it to indi- 
cate degrees, nor traces inscribed on its surface to guide 
us in such a course. The compass, though it affords a 
tolerable guide to the mariner or the traveller, is far too 
uncertain in its indications, and too little known in its laws, 
to be of any use in such an operation. We mast, therefore, 



OUTLINES OF ASTRONOMY 177 

look outward, and refer our situation on the surface of our 
globe to natural marks, external to it, and which are of 
equal permanence and stability with the earth itself. Such 
marks are afforded by the stars. By observations of their 
meridian altitudes, performed at any station, and from their 
known polar distances, We conclude the height of the pole; 
and since the altitude of the pole is equal to the latitude of 
the place (art. 119), the same observations give the latitudes 
of any stations where we may establish the requisite instru- 
ments. When our latitude, then, is found to have dimin- 
ished a degree, we know that, provided we have kept to the 
meridian, we have described one three hundred and sixtieth 
part of the earth's circumference. 

(212.) The direction of the meridian may be secured at 
every instant by the observations described in arts. 162, 
188; and although local difficulties may oblige us to de- 
viate in our measurement from this exact direction, yet if 
we keep a strict account of the amount of this deviation, 
a very simple calculation will enable us to reduce our ob- 
served measure to its meridional value. 

(213.) Such is the principle of that most important 
geographical operation, the measurement of an arc of the 
meridian. In its detail, however, a somewhat modified 
course must be followed. An observatory cannot be 
mounted and dismounted at every step; so that we cannot 
identify and measure an exact degree neither more nor less. 
But this is of no consequence, provided we know with 
equal precision how much, more or less, we have measured. 
In place, then, of measuring this precise aliquot part, we 
take the more convenient method of measuring from one 
good observing station to another, about a degree, or two 
or three degrees, as the case may be, or indeed any deter- 



178 OUTLINES OF ASTRONOMY 

minate angular interval apart, and determining by astro- 
nomical observation the precise difference of latitudes 
between the stations. 

(214.) Again, it is of great consequence to avoid in this 
operation every source of uncertainty, because an error com- 
mitted in the length of a single degree will be multiplied 360 
times in the circumference, and nearly 115 times in the 
diameter of the earth concluded from it. Any error which 
may affect the astronomical determination of a star's alti- 
tude will be especially influential. Now, there is still too 
much uncertainty and fluctuation in the amount of refrac- 
tion at moderate altitudes, not to make it especially desir- 
able to avoid this source of error. To effect this, we take 
care to select for observation, at the extreme stations, some 
star which passes through or near the zeniths of both. The 
amount of refraction, within a few degrees of the zenith, is 
very small, and, its fluctuations and uncertainty, in point of 
quantity, so excessively minute as to be utterly inappreci- 
able. Now, it is the same thing whether we observe the 
pole to be raised or depressed a degree, or the zenith distance 
of a star when on the meridian to have changed by the same 
quantity (fig. art. 128). If at one station we observe any 
star to pass through the zenith, and at the other to pass one 
degree south or north of the zenith, we are sure that the 
geographical latitudes, or the altitudes of the pole at the two 
stations, must differ by the same amount. 

(215.) Granting that the terminal points of one degree 
can be ascertained, its length may be measured by the meth- 
ods which will be presently described, as we have before 
remarked, to within a very few feet. Now, the error which 
may be committed in fixing each of these terminal points 
cannot exceed that which may be committed in the obser- 



OUTLINES OF ASTRONOMY 179 

vation of the zenith distance of a star properly situated for 
the purpose in question. This error, with proper care, can 
hardly exceed half a second. Supposing we grant the pos- 
sibility of ten feet of error in the length of each degree in a 
measured arc of five degrees, and of half a second in each of 
the zenith distances of one star, observed at the northern 
and southern stations, and, lastly, suppose all these errors 
to conspire, so as to tend all of them to give a result greater, 
or all less, than the truth, it will appear, by a very easy 
proportion, that the whole amount of error which would be 
thus entailed on an estimate of the earth's diameter, as 
concluded from such a measure, would not exceed 1147 
yards, or about two- thirds of a mile, and this is ample 
allowance. 

(216.) This, however, supposes that the form of the earth 
is that of a perfect sphere, and, in consequence, the lengths 
of its degrees in all parts precisely equal. But, when we 
come to compare the measures of meridional arcs made in 
various parts of the globe, the results obtained, although 
they agree sufficiently to show that the supposition of a 
spherical figure is not very remote from the truth, yet ex- 
hibit discordances far greater than what we have shown to 
be attributable to error of observation, and which render it 
evident that the hypothesis, in strictness of its wording, is 
untenable. The following table exhibits the lengths of arcs 
of the meridian (astronomically determined as above de- 
scribed), expressed in British standard feet, as resulting 
from actual measurement made with all possible care and 
precision, by commissioners of various nations, men of the 
first eminence, supplied by their respective governments 
with the best instruments, and furnished with every facility 
which could tend to insure a successful result of their im- 



180 



OUTLINES OF ASTRONOMY 



portant labors. The lengths of the degrees in the last col- 
umn are derived from the numbers set down in the two pre- 
ceding ones by simple proportion, a method not quite exact 
when the arcs are large, but sufficiently so for our purpose. 



















Mean 


















Length 


Country 


Latitude of 
Middle of Arc 


Arc 
measured 


Measured 

Length in 

Feet 


of the De- 
gree at 
the Mid- 
dle Lati- 


















tude in 


















Feet 


Sweden 1 , A B . 


+66° 


20' 


10" -o 


l e 


37' 


19" -6 


593277 


365744 


Sweden, A 






+66 


19 


37 





57 


30'4 


351832 


367086 


Russia, A 






+58 


17 


37 


3 


35 


52 


1309742 


365368 


Russia, B . 






+56 


3 


55-5 


8 


2 


28-9 


2937439 


365291 


Prussia, B 






+54 


58 


26-0 


1 


30 


29-0 


551073 


365420 


Denmark, B 






+54 


8 


13-7 


1 


31 


53-3 


559121 


365087 


Hanover, A B 






+52 


32 


16-6 


2 





57-4 


736425 


365300 


England, A 






+52 


35 


45 


3 


57 


13 1 


1442953 


364971 


England, B 






+52 


2 


19-4 


2 


50 


23 5 


1036409 


364951 


France, A 






+46 


52 


2 


8 


20 


0-3 


3040605 


364872 


France, A B 






+44 


51 


2-5 


12 


22 


12-7 


4509832 


364572 


Rome, A . 






+42 


59 


— 


2 


9 


47 


787919 


364262 


America, A 






+39 


12 


— 


1 


28 


45 


538100 


363786 


India, A B 






+16 


8 


21-5 


15 


57 


40-7 


6794598 


363044 


India, A B 






+12 


32 


20-8 


1 


34 


564 


574318 


362956 


Peru, A B 






— 1 


31 


0-4 


3 


7 


3-5 


1131050 


362790 


Cape of Good Hope, A 


—33 


18 


30 


1 


13 


17-5 


445506 


364713 


Cape of Good Hope, B 


—35 


43 


20-0 


3 


34 


34-7 


1301993 


364060 



It is evident from a mere inspection of the second and 
fifth columns of this table, that the measured length of afde- 
gree increases with the latitude, being greatest near the poles, 



1 The astronomers by whom 
follows : — 

• Sweden, A B — S van berg. 
Sweden, A — Maupertuis. 
Russia, A — Struve. 
Russia, B — Struve, Tenner. 
Prussia — Bessel, Bayer. 
Denmark — Schumacher. 
Hanover — Gauss. 
England — Roy, Kater. 
France, A — Lacaille, Cassini. 



these measurements were executed were 



France, A B — Delambre, Mechain. 
Rome — Boscovich. 
America — Mason and Dixon. 
India, 1st — Lambton, Everest. 
India, 2d — Lambton. 
Peru — Lacondamine, Bouguer. 
Cape of Good Hope, A — Lacaille. 
Cape of Good Hope, B — Maclear. 

— Astr. Nachr. 574. 



OUTLINES OF ASTRONOMY 181 

and least near the equator. Let us now consider what inter- 
pretation is to be put upon this conclusion, as regards the 
form of the earth. 

(217.) Suppose we held in our hands a model of the 
earth smoothly turned in wood, it would he, as already 
observed, so nearly spherical, that neither by the eye nor 
the touch, unassisted by instruments, could we detect any 
deviation from that form. Suppose, too, we were debarred 
from measuring directly across from surface to surface in 
different directions with any instrument, by which we might 
at once ascertain whether one diameter were longer than 
another ; how, then, we may ask, are we to ascertain whether 
it is a true sphere or not? It is clear that we have no 
resource, but to endeavor to 
discover, by some nicer means 
than simple inspection or feel- 
ing, whether the convexity of 
its surface is the same in every 
part; and if not, where it is 
greatest, and where least. Sup- 
pose, then, a thin plate of metal to be cut into a concavity 
at its edge, so as exactly to fit the surface at A : let this now 
be removed from A, and applied successively to several 
other parts of the surface, taking care to keep its plane 
always on a great circle of the globe, as here represented. 
If, then, we find any position B, in which the light can 
enter in the middle between the globe and plate, or any 
other, C, where the latter tilts by pressure, or admits the 
light under its edges, we are sure that the curvature of the 
surface at B is less, and at C greater, than at A. 

(218.) What we here do by the application of a metal 
plate of determinate length and curvature, we do on the 




182 OUTLINES OF ASTRONOMY 

earth by the measurement of a degree of variation in the 
altitude of the pole. Curvature of a surface is nothing but 
the continual deflection of its tangent from one fixed direc- 
tion as we advance along it. When, in the same measured 
distance of advance we find the tangent (which answers to 
our horizon) to have shifted its position with respect 
to a fixed direction in space (such as the axis of the 
heavens, or the line joining the earth's centre and some 
given star) more in one part of the earth's meridian than 
in another, we conclude, of necessity, that the curvature of 
the surface at the former spot is greater than at the latter; 
and vice versd } when, in order to produce the same change 
of horizon with respect to the pole (suppose 1°) we require 
to travel over a longer measured space at one point than at 
another, we assign to that point a less curvature. Hence 
we conclude that the curvature of a meridional section of the 
earth is sensibly greater at the equator than toward the poles; 
or, in other words, that the earth is not spherical, hut flat- 
tened at the poles, or, which comes to the same, protuberant 
at the equator. 

(219.) Let NABDEF represent a meridional section 
of the earth, C its centre, and 1ST A, B D, Gr E, arcs of a 
meridian, each corresponding to one degree of difference 
of latitude, or to one degree of variation in the meridian 
altitude of a star, as referred to the horizon of a spectator 
travelling along the meridian. Let n N, a A, b B, d D, 
g Gr, e E, be the respective directions of the plumb-line at 
the stations K, A, B, D, G, E, of which we will suppose 
N to be at the pole and E at the equator; then will the 
tangents to the surface at these points respectively be per- 
pendicular to these directions; and, consequently, if each 
pair, viz. n N and a A, b B and d D, g Gr and e E, be pro- 



OUTLINES OF ASTRONOMY 



183 



longed till they intersect each other (at the points x, y, s), 
the angles N x A, B y D, Gr z E, will each be one degree, 
and, therefore, all equal; so that the small curvilinear arcs 
N A, B D, G E, may be regarded as arcs of circles of one 
degree each, described about x, y, z, as centres. These are 
what in geometry are called centres of curvature, and the 
radii x N or x A, y B or y D, z G or z E, represent radii 
of curvature, by which the curvatures at those points are 
determined and measured. Now, as the arcs of different 



a 


• 


hi l 




7P t 


\ J 




™ — *» 




X 


+*>-** z ■ s 


"" — y 



circles, which subtend equal angles at their respective 
centres, are in the direct proportion of their radii, and as 
the arc N A is greater than B D, and that again than G E, 
it follows that the radius N x must be greater than B y, 
and B y than E z. Thus it appears that the mutual inter- 
sections of the plumb-lines will not, as in the sphere, all 
coincide in one point C, the centre, but will be arranged 
along a certain curve, x y z (which will be rendered more 
evident by considering a number of intermediate stations). 
To this curve geometers have given the name of the evolute 



184 OUTLINES OF ASTRONOMY 

of the curve N A B D Gr E, from whose centres of curvature 
it is constructed. 

(220.) In the flattening of a round figure at two opposite 
points, and its protuberance at points rectangularly situated 
to the former, we recognize the distinguishing feature of the 
elliptic form. Accordingly, the next and simplest suppo- 
sition that we can make respecting the nature of the merid- 
ian, since it is proved not to be a circle, is that it is an 
ellipse, or nearly so, having N S, the axis of the earth, for 
its shorter, and E F, the equatorial diameter, for its longer 
axis; and that the form of the earth's surface is that which 
would arise from making such a curve revolve about its 
shorter axis N S. This agrees well with the general course 
of the increase of the degree in going from 'the equator to 
the pole. In the ellipse, the radius of curvature at E, the 
extremity of the longer axis is the least, and at that of 
the shorter axis, the greatest it admits, and the form of its 
evolute agrees with that here represented. a Assuming, then, 
that it is an ellipse, the geometrical properties of that curve 
enable us to assign the proportion between the lengths of 
its axes which shall correspond to any proposed rate 
of variation in its curvature, as well as to fix upon their 
absolute lengths, corresponding to any assigned length of 
the degree in a given latitude. Without troubling the 
reader with the investigation (which may be found in any 
work on the conic sections), it will be sufficient to state 
the results which have been arrived at by the most sys- 
tematic combinations of the measured arcs which have hith- 
erto been made by geometers. The most recent is that of 



2 The dotted lines are the portions of the evolute belonging to the other 
quadrants. 



OUTLINES OF ASTRONOMY 185 

Bessel, 3 who by a combination of the ten arcs, marked B 
in our table, has concluded the dimensions of the terrestrial 
spheroid to be as follows: 

Feet Miles 

Greater or equatorial diameter .... = 41,847,192 = 7925-604 

Lesser or polar diameter = 41,707,314=7899-114 

Difference of diameters, or polar compression . = 139,768 = 26-471 
Proportion of diameters as 299-15 to 298-15. 

The other combination whose result we shall state, is 
that of Mr. Airy, 4 who concludes as follows: 

Feet Miles 

Equatorial diameter =41,847,426 = 7925-648 

Polar diameter =41,707,620 = 7899-170 

Polar compression = 139,806 — 26*478 

Proportion of diameters as 299-33 to 298-33. 

These conclusions are based on the consideration of those 
13 arcs, to which the letter A is annexed, 6 and of one other 
arc of 1° T 31" -1, measured in Piedmont by Plana and Car- 
lini, whose discordance with the rest, owing to local causes 
hereafter to be explained, arising from the exceedingly 
mountainous nature of the country, render the propriety 
of so employing it very doubtful. Be that as it may, the 
strikingly near accordance of the two sets of dimensions is 
such as to inspire the greatest confidence in both. The 
measurement at the Cape of Good Hope by Lacaille, also 
used in this determination, has always been regarded as 
unsatisfactory, and has recently been demonstrated by Mr. 
Th. Maclear to be erroneous to a considerable extent. The 
omission of the former, and the substitution for the latter, 
of the far preferable result of Maclear' s second measurement 



3 Schumacher's Astronomische Nachrichten, Nos. 333, 334, 335, 438(1841). 

4 Encyclopasdia Metropolitana, "Figure of the Earth" (1831). 

5 In those which have both A and B, the numbers used by Mr. Airy differ 
slightly from Bessel' s, which are those we have preferred. 



186 OUTLINES OF ASTRONOMY 

would induce, however, but a trifling change in the final 
result. 

(221.) Thus we see that the rough diameter of 8000 miles 
we have hitherto used, is rather too great, the excess being 
about 100 miles, or -g^th part. As convenient numbers to 
remember, the reader may bear in mind, that in our lati- 
tude there are just as many thousands of feet in a degree 
of the meridian as there are days in the year (365): that, 
speaking loosely, a degree is about 70 British statute miles, 
and a second about 100 feet; that the equatorial circumfer- 
ence of the earth is a little less than 25,000 miles. (24, 899), 
and the ellipticity or polar flattening amounts to one 300th 
part of the diameter. 

(222.) The two sets of results above stated are placed in 
juxtaposition, and the particulars given more in detail than 
may at first sight appear consonant, either with the general 
plan of this work, or the state of the reader's presumed ac- 
quaintance with the subject. But it is of importance that 
he should early be made to see how, in astronomy, results in 
admirable concordance emerge from data accumulated from 
totally different quarters, and how local and accidental 
irregularities in the data themselves become neutralized 
and obliterated by their impartial geometrical treatment. 
In the cases before us, the modes of calculation followed 
are widely different, and in each the mass of figures to be 
gone through to arrive at the result, enormous. 

(223.) The supposition of an elliptic form of the earth's 
section through the axis is recommended by its simplicity, 
and confirmed by comparing the numerical results we have 
just set down with those of actual measurement. When 
this comparison is executed, discordances, it is true, are 
observed, which, although still too great to be referred to 



OUTLINES OF ASTRONOMY 187 

error of measurement, are yet so small, compared to the 
errors which would result from the spherical hypothesis, 
as completely to justify our regarding the earth as an ellip- 
soid, and referring the observed deviations to either local 
or, if general, to comparatively small causes. [For § (223 a) 
see Note D.] 

(224.) Now, it is highly satisfactory to find that the 
general elliptical figure thus practically proved to exist, is 
precisely what ought theoretically to result from the rotation 
of the earth on its axis. For, let us suppose the earth a 
sphere, at rest, of uniform materials throughout, and ex- 
ternally covered with an ocean of equal depth in every 
part. Under such circumstances it would obviously be in 
a state of equilibrium) and the water on its surface would 
have no tendency to run one way or the other. Suppose, 
now, a quantity of its materials were taken from the polar 
regions, and piled up all around the equator, so as to pro- 
duce that difference of the polar and equatorial diameters 
of 26 miles which we know to exist. It is not less evident 
that a mountain ridge or equatorial continent, only, would 
be thus formed, down which the water would run into the 
excavated part at the poles. However solid matter might 
rest where it was placed, the liquid part, at least, would not 
remain there, any more than if it were thrown on the side 
of a hill. The consequence, therefore, would be the forma- 
tion of two great polar seas, hemmed in all round by equa- 
torial land. Now, this is by no means the case in nature. 
The ocean occupies, indifferently, all latitudes, with no 
more partiality to the polar than to the equatorial. Since, 
then, as we see, the water occupies an elevation above the 
centre no less than 13 miles greater at the equator than at 
the poles, and yet manifests no tendency to leave the 



188 



OUTLINES OF ASTRONOMY 



former and run toward the latter, it is evident that it must 
be retained in that situation by some adequate power. No 
such power, however, would exist in the case we have sup- 
posed, which is therefore not conformable to nature. In 
other words, the spherical form is not the figure of equilib- 
rium ; and therefore the earth is either not at rest, or is so 
internally constituted as to attract the water to its equatorial 
regions, and retain it there. For the latter supposition 
there is no prima facie probability, nor any analogy to 
lead us to such an idea. The former is in accordance with 
all the phenomena of the apparent diurnal motion of the 
heavens; and therefore, if it will furnish us with the power 
in question, we can have no hesitation in adopting it as 
the true one. 

(225.) Now, everybody knows that when a weight is 
whirled round, it acquires thereby a tendency to recede 
from the centre of its motion; which is 
called the centrifugal force. A stone 
whirled round in a sling is a common 
illustration; but a better, for our present 
purpose, will be a pail of water, suspended 
by a cord, and made to spin round, while 
the cord hangs perpendicularly. The sur- 
face of the water, instead of remaining 
horizontal, will become concave, as in the 
figure. The centrifugal force generates a 
tendency in all the water to leave the 
axis, and press toward the circumference; 
it is, therefore, urged against the pail, and 
forced up its sides, till the excess of height, 
and consequent increase of pressure downward, just counter- 
balances its centrif ugal force, and a state of equilibrium is 



vf 




OUTLINES OF ASTRONOMY 189 

attained. The experiment is a very easy and instructive 
one, and is admirably calculated to show how the form of 
equilibrium accommodates itself to varying circumstances. 
If, for example, we allow the rotation to cease by degrees, 
as it becomes slower we shall see the concavity of the water 
regularly diminish; the elevated outward portion will de- 
scend, and the depressed central rise, while all the time 
a perfectly smooth surface is maintained, till the rotation is 
exhausted, when the water resumes its horizontal state. 

(226.) Suppose, then, a globe, of the size of the earth, at 
rest, and covered with a uniform ocean, were to be set 
in rotation about a certain axis, at first very slowly, but by 
degrees more rapidly, till it turned round once in twenty- 
four hours; a centrifugal force would be thus generated, 
whose general tendency would be to urge the water at every 
point of the surface to recede from the axis. A rotation 
might, indeed, be conceived so swift, as to flirt the whole 
ocean from the surface, like water from a mop. But this 
would require a far greater velocity than what we now 
speak of. In the case supposed, the iveight of the water 
would still keep it on the earth; and the tendency to recede 
from the axis could only be satisfied, therefore, by the water 
leaving the poles, and flowing toward the equator; there 
heaping itself up in a ridge, just as the water in our pail 
accumulates against the side; and being retained in oppo- 
sition to its weight, or natural tendency toward the centre, 
by the pressure thus caused. This, however, could not 
take place without laying dry the polar portions of the 
land in the form of immensely protuberant continents; 
and the difference of our supposed cases, therefore, is 
this: — in the former, a great equatorial continent and polar 
seas would be formed ; in the latter, protuberant land would 



190 OUTLINES OF ASTRONOMY 

appear at the poles, and a zone of ocean be disposed around 
the equator. This would be the first or immediate effect. 
Let us now see what would afterward happen, in the two 
cases, if things were allowed to take their natural course. 

(227.) The sea is constantly beating on the land, grinding 
it down, and scattering its worn off particles and fragments, 
in the state of mud and pebbles, over its bed. Geological 
facts afford abundant proof that the existing continents 
have all of them undergone this process, even more than 
once, and been entirely torn in fragments, or reduced to 
powder, and submerged and reconstructed. Land, in this 
view of the subject, loses its attribute of fixity. As a mass 
it might hold together in opposition to forces which the 
water freely obeys; but in its state of successive or simul- 
taneous degradation, when disseminated through the water, 
in the state of sand or mud, it is subject to all the impulses 
of that fluid. In the lapse of time, then, the protuberant 
land in both cases would be destroyed, and spread over the 
bottom of the ocean, filling up the lower parts, and tending 
continually to remodel the surface of the solid nucleus, in 
correspondence with the form of equilibrium in both cases. 
Thus, after a sufficient lapse of time, in the case of an earth 
at rest, the equatorial continent, thus forcibly constructed, 
would again be levelled and transferred to the polar excava- 
tions, and the spherical figure be so at length restored. In 
that of an earth in rotation, the polar protuberances would 
gradually be cut down and disappear, being transferred 
to the equator (as being then the deepest sea), till the earth 
won Id assume by degrees the form we observe it to have — 
that of a flattened or oblate ellipsoid. 

(228.) We are far from meaning here to trace the process 
by which the earth really assumed its actual form; all we 



OUTLINES OF ASTRONOMY 191 

intend is, to show that this is the form to which, under 
the conditions of a rotation on its axis, it must tend] and 
which it would attain, even if originally and (so to speak) 
perversely constituted otherwise. 

(229.) But, further, the dimensions of the earth and the 
time of its rotation being known, it is easy thence to calcu- 
late the exact amount of the centrifugal force, 6 which, at 
the equator, appears to be -girth part of the force or weight 
by which all bodies, whether solid or liquid, tend to fall 
toward the earth. By this fraction of its weight, then, the 
sea at the equator is lightened, and thereby rendered sus- 
ceptible of being supported on a higher level, or more 
remote from the centre than at the poles, where no such 
counteracting force exists; and where, in consequence, the 
water may be considered as specifically heavier. Taking 
this principle as a guide, and combining it with the laws 
of gravity (as developed by Newton, and as hereafter to be 
more fully explained), mathematicians have been enabled 
to investigate, a priori, what would be the figure of equilib- 
rium of such a body, constituted internally as we have 
reason to believe the earth to be; covered wholly or par- 
tially with a fluid; and revolving uniformly in twenty-four 
hours; and the result of this inquiry is found to agree very 
satisfactorily with what experience shows to be the case. 
From their investigations it appears that the form of equi- 
librium is, in fact, no other than an oblate ellipsoid, of a 
degree of ellipticity very nearly identical with what is ob- 
served, and which would be no doubt accurately so, did 
we know, with precision, the internal constitution and 
materials of the earth. 

6 Newton's Principia, iii. Prop. 19. 



192 OUTLINES OF ASTRONOMY 

(230.) The confirmation thus incidentally furnished, of 
the hypothesis of the earth's rotation on its axis, cannot 
fail to strike the reader. A deviation of its figure from 
that of a sphere was not contemplated among the original 
reasons for adopting that hypothesis, which was assumed 
solely on account of the easy explanation it offers of the 
apparent diurnal motion of the heavens. Yet we see that, 
once admitted, it draws with it, as a necessary consequence, 
this other remarkable phenomenon, of which no other satis- 
factory account could be rendered. Indeed, so direct is 
their connection, that the ellipticity of the earth's figure 
was discovered and demonstrated by Newton to be a conse- 
quence of its rotation, and its amount actually calculated 
by him, long before any measurement had suggested such a 
conclusion. As we advance with our subject, we shall find 
the same simple principle branching out into a whole train of 
singular and important consequences, some obvious enough, 
others which at first seem entirely unconnected with it, and 
which, until traced by Newton up to this their origin, had 
ranked among the most inscrutable arcana of astronomy, 
as well as among its grandest phenomena. 

(231.) Of its more obvious consequences, we may here 
mention one which falls naturally within our present sub- 
ject. If the earth really revolve on its axis, this rotation 
must generate a centrifugal force (see art. 225), the effect 
of which must of course be to counteract a certain portion 
of the weight of every body situated at the equator, as com- 
pared with its weight at the poles, or in any intermediate 
latitudes. Now, this is fully confirmed by experience. 
There is actually observed to exist a difference in the 
gravity, or downward tendency, of one and the same body, 
when conveyed successively to stations in different lati- 



OUTLINES OF ASTRONOMY 193 

tudes. Experiments made with, the greatest care, and in 
every accessible part of the globe, have fully demonstrated 
the fact of a regular and progressive increase in the weights 
of bodies corresponding to the increase of latitude, and fixed 
its amount and the law of its progression. From these it 
appears, that the extreme amount of this variation of 
gravity, or the difference between the equatorial and polar 
weights of one and the same mass of matter, is 1 part in 
194 of its whole weight, the rate of increase in travelling 
from the equator to the pole being as the square of the sine 
of the latitude. 

(232.) The reader will here naturally inquire what is 
meant by speaking of the same body as having different 
weights at different stations; and, how such a fact, if true, 
can be ascertained. When we weigh a body by a balance 
or a steel -yard we do but counteract its weight by the equal 
weight of another body under the very same circumstances; 
and if both the body weighed and its counterpoise be re- 
moved to another station, their gravity, if changed at all, 
will be changed equally, so that they will still continue 
to counterbalance each other. A difference in the intensity 
of gravity could, therefore, never be detected by these 
means ; nor is it in this sense that we assert that a body 
weighing 194 pounds at the equator will weigh 195 at the 
pole. If counterbalanced in a scale or steel- yard at the 
former station, an additional pound placed in one or other 
scale at the latter would inevitably sink the beam. 

(233.) The meaning of the proposition may be thus ex- 
plained: — Conceive a weight x suspended at the equator 
by a string without weight passing over a pulley, A, and 
conducted (supposing such a thing possible) over other 

pulleys, such as B, round the earth's convexity, till the 
Astronomy — Vol. XIX. — 9 




194 OUTLINES OF ASTRONOMY 

other end hung down at the pole, and there sustained 
the weight y. If, then, the weights x and y were such as, 
at any one station, equatorial or polar, 
would exactly counterpoise each other 
on a balance, or when suspended side 
by side over a single .pulley, they would 
not counterbalance each other in this 
supposed situation, but the polar weight 
y would preponderate; and to restore 
the equipoise the weight x must be increased by ytj-th part 
of its quantity. 

(234.) The means by which this variation of gravity may 
be shown to exist, and its amount measured, are twofold 
(like all estimations of mechanical power) statical and dy- 
namical. The former consists in putting the gravity of a 
weight in equilibrium, not with that of another weight, but 
with a natural power of a different kind not liable to be 
affected by local situation. Such a power is the elastic 
force of a spring. Let A B C be a strong support of brass 
standing on the foot AED cast in one piece with it, into 
which is let a smooth plate of agate, D, which can be ad- 
justed to perfect horizontality by a level. At C let a spiral 
spring Gr be attached, which carries at its lower end a weight 
F, polished and convex below. The length and strength 
of the spring must be so adjusted that the weight F shall 
be sustained by it just to swing clear of contact with the 
agate plate in the highest latitude at which it is intended 
to use the instrument. Then,, if small weights be added 
cautiously, it may be made to descend till it just grazes the 
agate, a contact which can be made with the utmost imagi- 
nable delicacy. Let these weights be noted; the weight F 
detached; the spring Gr carefully lifted off its hook, and 



OUTLINES OF ASTRONOMY 



195 



secured, for travelling, from rust, strain, or disturbance, 
and the whole apparatus conveyed to a station in a lower 
latitude. It will then be found, on remounting it, that, 
although loaded with the same additional weights as before, 
the weight F will no longer have power enough to stretch 
the spring to the extent required for pro- B 

ducing a similar contact. More weights 
will require to be added; and the addi- 
tional quantity necessary will, it is evi- 
dent, measure the difference of gravity 
between the two stations, as exerted on 
the whole quantity of pendent matter, 
i.e. the sum of the weight of F and half 
that of the spiral spring itself. Granting 
that a spiral spring can be constructed 
of such strength and dimensions that a 
weight of 10,000 grains, including its 
own, shall produce an elongation of 10 inches without 
permanently straining it, 7 one additional grain will pro- 
duce a further extension of lo * o0 th of an inch, a quantity 
which cannot possibly be mistaken in such a contact as 
that in question. Thus we should be provided with the 
means of measuring the power of gravity at any station to 
within l0 * 00 th of its whole quantity. 

(235.) The other, or dynamical process, by which the 




7 Whether the process above described could ever be so far perfected and 
refined as to become a substitute for the use of the pendulum must depend on 
the degree of permanence and uniformity of action of springs, on the constancy 
or variability of the effect of temperature on their elastic force, on the possibility 
of transporting them, absolutely unaltered, from place to place, etc The great 
advantages, however, which such an apparatus and mode of observation would 
possess, in point of convenience, cheapness, portability, and expedition, over 
the present laborious, tedious, and expensive process, render the attempt well 
worth making. [See Note E.] 



196 OUTLINES OF ASTRONOMY 

force urging any given weight to the earth may be deter- 
mined, consists in ascertaining the velocity imparted by it 
to the weight when suffered to fall freely in a given time, 
as one second. This velocity cannot, indeed, be directly 
measured ; but indirectly, the principles of mechanics fur- 
nish an easy and certain means of deducing it, and, conse- 
quently, the intensity of gravity, by observing the oscilla- 
tions of a pendulum. It is proved from mechanical prin- 
ciples, 8 that, if one and the same pendulum be made 
to oscillate at different stations, or under' the influence 
of different forces, and the numbers of oscillations made in 
the same time in each case be counted, the intensities of the 
forces will be to each other as the squares of the numbers 
of oscillations made, and thus their proportion becomes 
known. For instance, it is found that, under the equator, 
a pendulum of a certain form and length makes 86,400 
vibrations in a mean solar day; and that, when transported 
to London, the same pendulum makes 86,535 vibrations in 
the same time. Hence we conclude, that the intensity of 
the force urging the pendulum downward at the equator 
is to that at London as (86,400) a to (86,535) 2 , or as 1 to 
1 -00315 ; or, in other words, that a mass of matter weighing 
in London 100,000 pounds, exerts the same pressure on the 
ground, or the same effort to crush a body placed below it, 
that 100,315 of the same pounds transported to the equator 
would exert there. 

(236.) Experiments of this kind have been made, as 
above stated, with the utmost care and minutest precaution 
to insure exactness in all accessible latitudes; and their 
general and final result has been, to give y^ for the fraction 

8 Newton's Principia, ii. Prop. 24. Cor. 3. 



OUTLINES OF ASTRONOMY 197 

expressing the difference of gravity at the equator and 
poles. Now, it will not fail to be noticed by the reader, 
and will, probably, occur to him as an objection against 
the explanation here given of the fact by the earth's rota- 
tion, that this differs materially from the fraction -^ express- 
ing the centrifugal force at the equator. The difference by 
which the former fraction exceeds the latter is -g-J-g-, a small 
quantity in itself, but still far too large, compared with the 
others in question, not to be distinctly accounted for, and 
not to prove fatal to this explanation if it will not render 
a strict account of it. 

(237.) The mode in which this difference arises affords 
a curious and -instructive example of the indirect influence 
which mechanical causes often exercise, and of which as- 
tronomy furnishes innumerable instances. The rotation of 
the earth gives rise to the centrifugal force; the centrifugal 
force produces an ellipticity in the form of the earth itself; 
and this very ellipticity of form modifies its power of attrac- 
tion on bodies placed at its surface, and thus gives rise to 
the difference in question. Here, then, we have the same 
cause exercising at once a direct and an indirect influence. 
The amount of the former is easily calculated, that of the 
latter with far more difficulty, by an intricate and profound 
application of geometry, whose steps we cannot pretend to 
trace in a work like the present, and can only state its 
nature and result. 

(238.) The weight of a body (considered as undiminished 
by a centrifugal force) is the effect of the earth's attraction 
on it. This attraction, as Newton has demonstrated, con- 
sists, not in a tendency of all matter to any one particular 
centre, but in a disposition of every particle of matter in 
the universe to press toward, and if not opposed to approach 



198 OUTLINES OF ASTRONOMY 

to, every other. The attraction of the earth, then, on a 
body placed on its surface, is not a simple but a complex 
force, resulting from the separate attractions of all its parts. 
Now, it is evident, that if the earth were a perfect sphere, 
the attraction exerted by it on a body placed anywhere on 
its surface, whether at its equator or pole, must be exactly 
alike — for the simple reason of the exact symmetry of the 
sphere in every direction. It is not less evident that, the 
earth being elliptical, and this symmetry or similitude of 
all its parts not existing, the same result cannot be expected. 
A body placed at the equator, and a similar one at the pole 
of a flattened ellipsoid, stand in a different geometrical rela- 
tion to the mass as a whole. This difference, without enter- 
ing further into particulars, may be expected to draw with 
it a difference in its forces of attraction on the two bodies. 
Calculation confirms this idea. It is a question of purely 
mathematical investigation, and has been treated with per- 
fect clearness and precision by Newton, Maclaurin, Clairaut, 
and many other eminent geometers; and the result of their 
investigations is to show that, owing to the elliptic form of 
the earth alone, and independent of the centrifugal force, 
its attraction ought to increase the weight of a body in going 
from the equator to the pole by almost exactly -g^th part; 
which, together with -g^-g-th due to the centrifugal force, make 
up the whole quantity, y^th, observed. 

(239.) Another great geographical phenomenon, which 
owes its existence to the earth's rotation, is that of the 
trade- winds. These mighty currents in our atmosphere, on 
which so important a part of navigation depends, arise from, 
1st, the unequal exposure of the earth's surface to the sun's 
rays, by which it is unequally heated in different latitudes: 
and, 2dly, from that general law in the constitution of all 



OUTLINES OF ASTRONOMY 199 

fluids, in virtue of which they occupy a larger bulk, and 
become specifically lighter when hot than when cold. These 
causes, combined with the earth's rotation from west to east, 
afford an easy and satisfactory explanation of the magnifi- 
cent phenomena in question. 

(240.) It is a matter of observed fact, of which we shall 
give the explanation further on, that the sun is constantly 
vertical over some one or other part of the earth between 
two parallels of latitude, called the tropics, respectively 23-§° 
north, and as much south of the equator; and that the whole 
of that zone or belt of the earth's surface included between 
the tropics, and equally divided by the equator, is, in conse- 
quence of the great altitude attained by the sun in its diurnal 
course, maintained at a much higher temperature than those 
regions to the north and south which lie nearer the poles. 9 
Now, the heat thus acquired by the earth's surface is com- 
municated to the incumbent air, which is thereby expanded, 
and rendered specifically lighter than the air incumbent on 
the rest of the globe. It is, therefore, in obedience to the 
general laws of hydrostatics, displaced and buoyed up from 
the surface, and its place occupied by colder, and therefore 
heavier ,air, which glides in, on both sides, along the sur- 
face, from the regions beyond the tropics; while the dis- 
placed air, thus raised above its due level, and unsustained 
by any lateral pressure, flows over, as it were, and forms an 
upper current in the contrary direction, or toward the poles; 
which, being cooled in its course, and also sucked down to 
supply the deficiency in the extra-tropical regions, keeps 
up thus a continual circulation. That this is a real cause 



9 First distinctly delivered by Hadley, though often erroneously attributed 
to Edmund Halley, whose theory of the trade winds is altogether erroneous. 
(See Dove, Meteorol. Untersuchungen, p. 237.) 



200 OUTLINES OF ASTRONOMY 

(vera causa) is placed in complete evidence by the genera] 
fact that the atmospheric pressure at the surface of the sea 
diminishes regularly from either tropic to the equator, 
where the barometer stands habitually about 0^.2 lower 
than in the temperate zones. 

(241.) Since the earth revolves about an axis passing 
through the poles, the equatorial portion of its surface has 
the greatest velocity of rotation, and all other parts less in 
the proportion of the radii of the circles of latitude to which 
they correspond. But as the air, when relatively and ap- 
parently at rest on any part of the earth's surface, is only 
so because in reality it participates in the motion of rotation 
proper to that part, it follows that when a mass of air near 
the poles is transferred to the region near the equator by 
any impulse urging it directly toward that circle, in every 
point of its progress toward its new situation it must be 
found deficient in rotatory velocity, and therefore unable 
to keep up with the speed of the new surface over which 
it is brought. Hence, the currents of air which set in 
toward the equator from the north and south must, as 
they glide along the surface, at the same time lag, or hang 
back, and drag upon it in the direction opposite to the earth's 
rotation, i.e. from east to west. Thus these currents, which 
but for the rotation would be simply northerly and southerly 
winds, acquire, from this cause, a relative direction toward 
the west, and assume the character of permanent north- 
easterly and southeasterly winds. 

(242.) Were any considerable mass of air to be suddenly 
transferred from beyond the tropics to the equator, the 
difference of the rotatory velocities proper to the two situa- 
tions would be so great as to produce not merely a wind, 
but a tempest of the most destructive violence. But this 



OUTLINES OF ASTRONOMY 201 

is not the case: the advance of the air from the north and 
south is gradual, and all the while the earth is continually 
acting on, and by the friction of its surface accelerating 
its* rotatory velocity. Supposing its progress toward the 
equator to cease at any point, this cause would almost im- 
mediately communicate to it the deficient motion of rota- 
tion, after which it would revolve quietly with the earth, 
and be at relative rest. We have only to call to mind the 
comparative thinness of the coating which the atmosphere 
forms around the globe (art. 35), and the immense mass 
of the latter, compared with the former (which it exceeds 
at least 1,200,000 times), to appreciate fully the influence of 
any extensive territory of the earth over the atmosphere 
immediately incumbent on it, in destroying any impulse 
once given to it, and which is not continually renewed. 
(243.) It follows from this, then, that as the winds on 
both sides approach the equator, their easterly tendency 
must diminish. l0 The lengths of the diurnal circles increase 
very slowly in the immediate vicinity of the equator, and 
for several degrees on either side of it hardly change at all. 
Thus the friction of the surface has more time to act in 
accelerating the velocity of the air, bringing it toward 
a state of relative rest, and diminishing thereby the relative 
set of the currents from east to west, which, on the other 
hand, is feebly, and, at length, not at all, reinforced by the 
cause which originally produced it. Arrived, then, at the 
equator, the trades' must be expected to lose their easterly 
character altogether. But not only this, but the northern 
and southern currents here meeting and opposing, will 

10 See Captain Hall's "Fragments of Voyages and Travels, " 2d series, vol. i., 
p. 162, where this is very distinctly, and, so far as I am aware, for the first 
time, reasoned out. 



202 OUTLINES OF ASTRONOMY 

mutually destroy each, other, leaving only such preponder- 
ancy as may be due to a difference of local causes acting 
in the two hemispheres — which in some regions around the 
equator may lie one way, in some another. 

(244.) The result, then, must be the production of two 
great tropical belts, in the northern of which a constant 
northeasterly, and in the southern a southeasterly, wind 
must prevail, while the winds in the equatorial belt, which 
separates the two former, should be comparatively calm 
and free from any steady prevalence of easterly character. 
All these consequences are agreeable to observed fact, and 
the system of aerial currents above described constitutes in 
reality what is understood by the regular trade winds. 

(245.) The constant friction thus produced between the 
earth and atmosphere in the regions near the equator must 
(it may be objected) by degrees reduce and at length destroy 
the rotation of the whole mass. The laws of dynamics, 
however, render such a consequence, generally, impossible; 
and it is easy to see, in the present case, where and how 
the compensation takes place. The heated equatorial air, 
while it rises and flows over toward the poles, carries with 
it the rotatory velocity due to its equatorial situation into 
a higher latitude, where the earth's surface has less motion. 
Hence, as it travels northward or southward, it will gain 
continually more and more on the surface of the earth in 
its diurnal motion, and assume constantly more and more a 
westerly relative direction; and when at length it returns 
to the surface, in, its circulation, which it must do more or 
less in all the interval between the tropics and the poles, 
it will act on it by its friction as a powerful southwest wind 
in the northern hemisphere, and a northwest in the southern, 
and restore to it the impulse taken up from it at the equator. 



OUTLINES OF ASTRONOMY 203 

We have here the origin of the southwest and westerly gales 
so prevalent in our latitudes, and of the almost universal 
westerly winds in the North Atlantic, which are, in fact, 
nothing else than a part of the general system of the re- 
action of the trades, and of the process by which the equi- 
librium of the earth's motion is maintained under their 
action. 

(245 a.) If in any region of the earth's surface, where 
the latitude is considerable, and where, in consequence, the 
circumference of the diurnal circles described by points on 
the same meridian a few degrees asunder differ considerably, 
an impulse (from whatever cause arising) from the pole 
toward the equator be communicated to a portion of the 
atmosphere covering several square degrees; an observer 
situated on the equatorial limit of the area so disturbed will, 
in the first instant of the disturbance, experience a wind 
blowing directly from the pole, i.e. a north wind in the 
northern hemisphere and a south in the southern. To fix 
our ideas, suppose him situate in north latitude and beyond 
the tropic. The air which reaches him in the first instant, 
arising from a place in his immediate vicinity, has the same 
diurnal rotatory velocity with himself, and will therefore 
have no relative movement westward. But the southward 
movement of the whole mass of air continuing, the wind 
which subsequently reaches his station arriving from lati- 
tudes continually more and more north, and therefore set- 
ting out with a rotatory velocity continually more and more 
inferior to that of the observer, will lag more and more be- 
hind the easterly motion of the earth' s surface at his station, 
and will therefore become, relatively to him, more and more 
of an east wind. In other words, a wind commencing to 
blow from the north will not continue long to do so, but 



204 OUTLINES OF ASTRONOMY 

will "draw toward the east," veering gradually round to 
1ST. N. E. and N. E. ; vice versa if the impulse of the mass 
of air be from south to north. The first impression on the 
observer will be that of a south wind, which in the progress 
of time will veer round through S.S.W. to S.W., and so 
mutatis mutandis in the other hemisphere; and thus arises 
a general tendency of the wind in extra- tropical latitudes 
to veer in a fixed direction, or "to follow the sun, ' ' which 
meteorological observation very decisively confirms as a 
matter of fact, and is therefore pro tanto a proof of the 
reality of the assigned cause. 11 

(245 b.) It is, however, in those tremendous visitations 
called "hurricanes," which sweep across land and sea with 
a devastating power exceeded only by the earthquake, that 
we find the most striking verification of the principle above 
stated. Suppose that in any locality in the northern hemi- 
sphere some considerable portion of the surface, whether of 
sea or land, should become so much more heated by the 
sun's rays than that surrounding it, as to determine an up- 
ward movement in the air above it in the nature of an 
ascending column, thereby giving rise to a diminished 
barometric pressure, and as a necessary consequence to 
an indraught of air from all quarters toward the heated 
area. Those portions which arrive from the east and west, 
participating in the entire diurnal movement corresponding 
to the latitude, will simply meet and be hurried upward, 
without any tendency to gyrate round a centre. But the 
portions which arrive from the northward will all reach 
the heated region or its immediate confines with a modified 
power. Those which come from the northeasterly quadrant 

11 See Article Meteorology, Encyc. Brit. § 70. 



OUTLINES OF ASTRONOMY 205 

will have their westerly force increased, and those from the 
northwest quadrant, their easterly force diminished, so that 
in arriving from the northward, the general current setting 
to the heated region will have assumed a tendency from 
east to west, and in arriving from the southward from 
west to east, and these portions being drawn up together 
into the ascending column, will necessarily assume a rota- 
tion round its general axis in the direction N.W.S.E., 12 
whereas, were the earth at rest, the air coming in from all 
quarters with equal force, each particle would make direct 
for the centre, and simply be thrown up vertically without 
any gyration. 

(245 c.) The rotation thus given to the ascending column 
in the northern hemisphere is in a direction contrary to that 
of the hands of a watch face upward, which we may term 
retrograde. And by a similar reasoning, in the southern 
it will be seen that a contrary, or direct rotation ought to 
arise from the operation of the same causes. It is, more- 
over, obvious, that the energy of the vortex so produced 
must be, cceteris paribus, proportional to that of its efficient 
causes. In high latitudes there is a deficiency of solar 
heat to produce a powerful ascensional current. On and 
about the equator, on the other hand, though heat be 
abundant, the other efficient cause, viz. a considerable 
difference of diurnal rotatory velocity, is absent. Such 
movements, therefore, cannot exist on the equator, and 
their intensity will chiefly be confined to regions in 
moderate latitudes. 

(245 d.) Now every one of these particulars is in exact 



12 See Encyclop. Brit. Meteorology, § 73, for the complete reasoning out of 
tnis process. 



206 OUTLINES OF ASTRONOMY 

conformity with the history of those hurricanes, or cyclones, 
as they have been called, from their revolving character, 
which infest the Atlantic along the east coasts of the United 
States and the West Indies, the Indian Ocean, and (under 
the name of typhoons) the China seas. Their extent and 
violence are frightful; their rotation in the same hemi- 
sphere is invariably the same, and in each, that which 
theory indicates; and they are utterly wanting on the 
equator. This grand result, the establishment of which 
we owe to the labors of Mr. Kedfield, Sir W. Eeid, and 
Mr. Piddington, forms a capital feature in the array of 
evidence by which the rotation of the earth, as a physical 
fact, is demonstrated. 

(245 e.) Another class of phenomena, inexplicable ex- 
cept on the hypothesis of the earth's rotation on its axis, 
but flowing easily and naturally from the admission of that 
principle, has, within a few years from the present time, 
been brought under our inspection by M. Foucault. If a 
heavy mass of metal (a globe of lead, for example) be sus- 
pended by a long wire from a solid and perfectly fixed sup- 
port, over the centre of a plane table of a circular form, and, 
being drawn aside from the perpendicular (suppose in the 
direction of the meridian), be then allowed to oscillate, tak- 
ing extreme care to avoid giving it any lateral motion (which 
may be accomplished by drawing it aside by a fine thread, 
and, when quite at rest, burning off the thread), it will of 
course commence its oscillations in the plane of the merid- 
ian. But when watched attentively, marking on the table 
the points of its circumference, from time to time, opposite 
to its points of extreme excursion, it will in a few minutes 
be seen to have (apparently) shifted its plane of motion; the 
northern extremity of its excursions to and fro having inva- 



OUTLINES OF ASTRONOMY 



207 



riably gone round in azimuth toward the east, and the southern 
toivard the west [supposing the experiment made in the northern 
hemisphere — vice versa in the southern). Although, in a few 
oscillations the deviation is too small to be readily per- 
ceived, it at length becomes apparent that the path traced 
on the table by the projection of the centre of the globe, in- 
stead of being a rigorous straight line, as it must be accord- 
ing to the laws of dynamics, were the table at rest, is, in 




reality, a looped curve of the form here shown [fig. a) (the 
intervals of the loops being much exaggerated) ; all of them 
passing through the centre of the table. 

(245 /. ) It is evident that such a motion is quite different 
from that which a small lateral motion accidentally commu- 
nicated to the pendulous body would produce. The effect 
of such an impulse would be to make the central mass de- 
scribe a series of elongated ovals, a kind of elliptic spiral, 
the convolutions of which would pass, not through, but 



208 



OUTLINES OF ASTRONOMY 



round the centre, as here represented (/£#. b)\ and that in- 
differently in one direction or the other, according to the 
accident of the lateral impulse. On the other hand, the 
observed effect is precisely such as would take place, sup- 
posing the plane of oscillation to remain invariable, and the 
table to revolve beneath it in its own plane in a contrary 
direction (from north to west), with an angular motion duly 
adjusted. Supposing the oscillating ball to leave a trace on 
the table so turning, that trace would evidently be such a 

jw?. a. 




one as described in the preceding article; and if we admit 
the rotation of the earth, it is a fact that the table, though 
unperceived by us, does so turn. It is not transferred by 
the earth's rotation bodily to the eastward by a parallel 
movement of all its parts. The southern extremity of its 
meridional diameter S is carried in a given time (suppose one 
minute) more to the eastward than the northern ; so that it 
has virtually rotated in its own plane through an angle cor- 
responding to the difference of these two movements of 
transference. 



OUTLINES OF ASTRONOMY 209 

(245 g.) This difference is a maximum at the pole (where 
it is obvious that the table turns entirely in its own plane, 
as the earth's surface there does); and it is nil at the 
equator, where, in consequence, the experiment would be 
made in vain (the entire rotation of the table there being in 
a plane perpendicular to its own) ; and generally the effect 
will be more strikingly developed in high than in low lati- 
tudes. To show this more clearly, suppose P the north 
pole, C the centre of the earth, C P Q its axis prolonged, 
A B two successive positions of the table at an interval of 
one minute of time, during which the 
meridian A P has rotated through an 
angle of 0° 15' round P to the position 
B P. The plane of the table, being a 
tangent to the earth's surface, will, if 
produced (whether it be at A or B), 
meet the axis at Q, the vertex of a 
cone having for its base the diurnal 
circle of the place of observation. Dur- 
ing the small interval in question, the 
portion A Q B of this conical surface 
may be regarded as plane, and the motion of the table will 
be the same as if it formed a part of that plane, and revolved 
round a pivot at Q, the meridional diameter a a being trans- 
ferred into the position b b, making with a a an angle equal 
to A Q B. Now this angle at the equator is nil, the summit 
of the cone being there infinitely remote; whereas, on the 
pole it is identical with the spherical angle A P B, the 
table there rotating about its own centre. 

(245 h.) The gyroscope is an instrument devised by M. 
Foucault to exhibit the same sort of effect in another man- 
ner. It depends on the very obvious principle that a body 




210 



OUTLINES OF ASTRONOMY 



revolving round one. of its axes of permanent rotation, and 
free from any disturbing attachment to surrounding objects, 
will preserve its plane of rotation unaltered. Imagine a 
metallic disk, thin in the centre but very thick at the cir- 
cumference so as to present in section the figure A B, to be 
fixed on an axis C D, perpendicular to its plane which turns 




in pivot holes C D, on opposite ends of the diameter of a 
ring of metal, which is itself provided with exterior pivots 
on the extremities of a diameter at right angles to the 
former, and let these rest in pivot holes B F, at the lower 
ends of a semicircular metallic arc E Gr F, supported from 
its middle G by a torsionless suspension, such as may be 
formed by attaching a thread to a hook at the lower end of 
a steel arm, terminating in an inverted conical point resting 



OUTLINES OF ASTRONOMY 211 

in a polished agate cup as at H. The whole of this appa- 
ratus is to be executed with extreme delicacy, and with 
every precaution to secure perfect equilibrium and freedom 
from friction in the pivots. Suppose now that by some 
sufficient mechanical means an exceedingly rapid rotation 
is communicated to the disk which is then abandoned to 
itself. It is evident then, 1st, that it may be set in rotation 
originally in any given plane, and, 2dly, that however that 
initial plane be situated, it will thenceforward continue to 
rotate in that plane, since the mode of suspension is such as 
to exercise no control over it, in that respect. If the disk 
be heavy, the initial rotation very rapid (and especially if 
suspended in vacuo) the motion will be kept up for a con- 
siderable time — quite long enough to exhibit the phenomena 
due to the earth's rotation. 

(245 i.) There being no action exerted by either the 
pivots or the suspension which can affect the plane of rota- 
tion, this will necessarily continue unchanged, so that the 
axis C D about which it spins will remain parallel to itself, 
however the point of suspension may be varied in place by 
bodily transfer of the whole apparatus, or in relative posi- 
tion by change in the absolute direction of gravity conse- 
quent on the earth's diurnal rotation. Suppose then the 
axis CD to point at any instant to a given fixed star, then 
if the earth were at rest and the diurnal movement of the 
starry heavens real, it could not continue so to point, since 
the star would move away out of its line of direction, and 
would appear to leave it behind. The contrary however is 
the case. The axis of the disk continues to point to the star 
so long as the disk itself continues to revolve, and, could its 
rotation be kept up for twenty-four hours, would doubtless 
continue to follow it through its whole diurnal circle both 



212 OUTLINES OF ASTRONOMY 

above and below the horizon, affording thus a clear ocular 
demonstration of the earth's rotation, since if a line, of 
whose fixity of direction we are d priori sure, appear to vary 
in position with respect to the visible horizon and surround- 
ing objects it cannot be but that that horizon and those ter- 
restrial points of reference have, themselves, shifted in posi- 
tion by a corresponding opposite movement. 

(245 j.) If the conditions of suspension be such as to 
limit the axis of rotation of the disk to a plane holding a 
determinate position with respect to the horizon, as, for 
instance, that of the horizon itself, or of the meridian of the 
place, its movements are in conformity with what the prin- 
ciples of dynamics indicate as the result of a composition of 
the free rotation of the disk and that of the earth so partially 
communicated to it. We shall not however pursue the sub- 
ject into these details. The student will find them lucidly 
explained by Professor Powell, in the monthly notices of 
the Astronomical Society for April, 1855. The mechanical 
fact on which the whole theory turns (the powerful resist- 
ance opposed by a rapidly revolving heavy body to a change 
of position in its axis of rotation) may be brought under the 
evidence of the senses by the following simple and elegant 
experiment. Let any one detach an 18-inch terrestrial globe 
from its wooden frame, and, holding it by the brass merid- 
ian with the plane of that circle horizontal, let a rapid rota- 
tion be given to the globe by an assistant. So long as no 
attempt is made to alter the position of the axis, the only 
sensation experienced by the holder will be the effort of sus- 
taining the weight of the globe, just as if it were at rest. 
But so soon as he attempts to shift the direction of the axis, 
whether in a horizontal, a vertical, or any other plane, he 
will at once become aware of a resistance in the revolving 



OUTLINES OF ASTRONOMY 213 

globe to such a change, quite different from the simple iner- 
tia of a globe at rest — a kind of internal struggle — an effort 
to twist the globe in his hands, as if some animal were in- 
closed within its hollow, or as if it were no longer equally 
balanced on its centre. If he endeavor to roll the globe on 
its brass meridian in a right line along the floor (which with 
a non- rotating globe would be easy) he will find it imprac- 
ticable without perpetually and forcibly interfering, not 
merely to keep the meridian upright but to prevent its run- 
ning out of the right line. Suppose, for instance, the brass 
meridian to be vertical and its plane coincident with that of 
the true meridian, the axis horizontal, and the globe to 
rotate in the direction in which the heavens appear to re- 
volve, i.e. from the east upward; to the west downward, and 
let him attempt to roll it (lightly held by the finger and 
thumb by the highest point of the circle) in a northerly 
direction. He will find it run round to the eastward, caus- 
ing the plane of the brass meridian to shift in azimuth in a 
direction similar to that of the hands of a watch, and vice 
versa if he try to make it roll southward. That end of the 
axis which rises appears to be swept along with the revolv- 
ing motion of the globe as seen from above. 

(216.) In order to construct a map or model of the earth, 
and obtain a knowledge of the distribution of sea and land 
over its surface, the forms of the outlines of its continents 
and islands, the courses of its rivers and mountain chains, 
and the relative situations, with respect to each other, of 
those points which chiefly interest us, as centres of human 
habitation, or from other causes, it is necessary to possess 
the means of determining correctly the situation of any pro- 
posed station on its surface. For this two elements require 
to be known, the latitude and longitude, the former assign* 



214 OUTLINES OF ASTRONOMY 

ing its distance from the poles or the equator, the latter, the 
meridian on which that distance is to be reckoned. To 
these, in strictness, should be added, its height above the 
sea level; but the consideration of this had better be de- 
ferred, to avoid complicating the subject. 

(247.) The latitude of a station on a sphere would be 
merely the length of an arc of the meridian, intercepted 
between the station and the nearest point of the equator, 
reduced into degrees. (See art. 88.) But as the earth is 
elliptic, this mode of conceiving latitudes becomes inappli- 
cable, and we are compelled to resort for our definition of 
latitude to a generalization of that property (art. 119), which 
affords the readiest means of determining it by observation, 
and which has the advantage of being independent of the 
figure of the earth, which, after all, is not exactly an ellip- 
soid, or any known geometrical solid. The latitude of a 
station, then, is the altitude of the elevated pole, and is, 
therefore, astronomically determined by those methods al- 
ready explained for ascertaining that important element. 
In consequence, it will be remembered that, to make a per- 
fectly correct map of the whole, or any part of the earth's 
surface, equal differences of latitude are not represented by 
exactly equal intervals of surface. 

(248.) For the purposes of geodesical 18 measurements and 
trigonometrical surveys, an exceedingly correct determina- 
tion of the latitudes of the most important stations is re- 
quired. For this purpose, therefore, the zenith sector (an 
instrument capable of great precision) is most commonly 
used to observe stars passing the meridian near the zenith, 
whose declinations have become known by previous long 

13 Trj, the earth ; 6e<n« (from Sew, to bind), a joining or connection (of parts). 



OUTLINES OF ASTRONOMY 



215 



series of observations at fixed observatories, and which are 
therefore called standard or fundamental stars. Eecentlj a 
method 14 has been employed with great success, which con- 
sists in the use of an instrument similar in every respect to 
the transit instrument, but having the plane of motion of the 
telescope not coincident with the meridian, but with the 
prime vertical, so that its axis of rotation prolonged passes 
through the north and south points of the horizon. Let 
A B C D be the celestial hemisphere projected on the hori- 




zon, P the pole, Z the zenith, A B the meridian, C D the 
prime vertical, Q E S part of the diurnal circle of a star 
passing near the zenith, whose polar distance P E is but lit- 
tle greater than the co-latitude of the place, or the arc P Z, 
between the zenith and pole (art. 112). Then the moments 
of this star's arrival on the prime vertical at Q and S will, 
if the instrument be correctly adjusted, be those of its cross- 
ing the middle wire in the field of view of the telescope (art. 



14 Devised originally by Romer. Revived or re-invented by Bessel. — Astr. 
Nachr., No. 40. 



216 OUTLINES OF ASTRONOMY 

160). Consequently the interval between these moments 
will be the time of the star passing from Q to S, or the 
measure of the diurnal arc QES, which corresponds to the 
angle Q P S at the pole. This angle, therefore, becomes 
known by the mere observation of an interval of time, in which 
it is not even necessary to know the error of the clock, and 
in which, when the star passes near the zenith, so that the 
interval in question is small, even the rate of the clock, or 
its gain or loss on true sidereal time, may be neglected. 
Now the angle Q P S, or its half Q P E, and P Q the polar 
distance of the star, being known, P Z the zenith distance 
of the pole can be calculated by the resolution of the right- 
angled spherical triangle P Z Q, and thus the co- latitude 
(and of course the latitude) of the place of observation be- 
comes known. The advantages gained by this mode of ob- 
servation are, 1st, that no readings of a divided arc are 
needed, so that errors of graduation and reading are 
avoided: 2dly, that the arc Q E S is very much greater 
than its versed sine E Z, so that the difference E Z between 
the latitude of the place and the declination of the star is 
given by the observation of a magnitude very much greater 
than itself, or is, as it were, observed on a greatly enlarged 
scale. In consequence, a very minute error is entailed on 
E Z by the commission of even a considerable one in Q E S : 
3dly, that in this mode of observation all the merely instru- 
mental errors which affect the ordinary use of the transit 
instrument are either uninfluential or eliminated by simply 
reversing the axis. 

(249.) To determine the latitude of a station, then, is 
easy. It is otherwise with its longitude, whose exact deter- 
mination is a matter of more difficulty. The reason is this: 
— as there are no meridians marked upon the earth, any 



OUTLINES OF ASTRONOMY 217 

more than parallels of latitude, we are obliged in this case, 
as in the case of the latitude, to resort to marks external to 
the earth, i.e. to the heavenly bodies, for the objects of our 
measurement; but with this difference in the two cases — to 
observers situated at stations on the same meridian {i.e. dif- 
fering in latitude) the heavens present different aspects at 
all moments. The portions of them which become visible 
in a complete diurnal rotation are not the same, and stars 
which are common to both describe circles differently in- 
clined to their horizons, and differently divided by them, 
and attain different altitudes. On the other hand, to ob- 
servers situated on the same parallel (i.e. differing only in 
longitude) the heavens present the same aspects. Their 
visible portions are the same; and the same stars describe 
circles equally inclined, and similarly divided by their hori- 
zons, and attain the same altitudes. In the former case 
there is, in the latter there is not, anything in the appear- 
ance of the heavens, watched through a whole diurnal 
rotation, which indicates a difference of locality in the 
observer. 

(250.) But no two observers, at different points of the 
earth's surface, can have at the same instant the same celes- 
tial hemisphere visible. Suppose, to fix our ideas, an ob- 
server stationed at a given point of the equator, and that at 
the moment when he noticed some bright star to be in his 
zenith, and therefore on his meridian, he should be sud- 
denly transported, in an instant of time, round one quarter 
of the globe in a westerly direction, it is evident that he will 
no longer have the same star vertically above him: it will 
now appear to him to be just rising, and he will have to wait 
six hours before it again comes to his zenith, i.e. before the 

earth's rotation from west to east carries him back again to 
Astronomy — Vol. XIX.— 10 



218 OUTLINES OF ASTRONOMY 

the line joining the star and the earth's centre from which 
he set out. 

(251.) The difference of the cases, then, may be thus 
stated, so as to afford a key to the astronomical solution of 
the problem of the longitude. In the case of stations differ- 
ing only in latitude, the same star comes to the meridian at 
the same lime, but at different altitudes. In that of stations 
differing only in longitude, it comes to the meridian at the 
same altitude, but at different times. Supposing, then, that 
an observer is in possession of any means by which he can 
certainly ascertain the time of a known star's transit across 
his meridian, he knows his longitude; or if he knows the 
difference between its time of transit across his meridian and 
across that of any other station, he knows their difference of 
longitudes. For instance, if the same star pass the meridian 
of a place A at a certain moment, and that of B exactly one 
hour of sidereal time, or one twenty- fourth part of the 
earth's diurnal period, later, then the difference of longi- 
tude between A and B is one hour of time or 15° of arc, 
and B is so much west of A. 

(252.) In order to have a perfectly clear understanding 
of the principle on which the problem of finding the longi- 
tude by astronomical observations is resolved, the reader 
must learn to distinguish between time, in the abstract, as 
common to the whole universe, and therefore reckoned from 
an epoch independent of local situation, and local time, 
which reckons, at each particular place, from an epoch, or 
initial instant, determined by local convenience. Of time 
reckoned in the former, or abstract manner, we have an 
example in what we have before defined as equinoctial time, 
which dates from an epoch determined by the sun's motion 
among the stars. Of the latter, or local reckoning, we have 



OUTLINES OF ASTRONOMY 219 

instances in every sidereal clock in an observatory, and in 
every town clock for common use. Every astronomer regu- 
lates, or aims at regulating, his sidereal clock, so that it shall 
indicate h m 3 , when a certain point in the heavens, called 
the equinox, is on the meridian of his station. This is the 
epoch of his sidereal time; which is, therefore, entirely a 
local reckoning. It gives no information to say that an 
event happened at such and such an hour of sidereal time, 
unless we particularize the station to which the sidereal time 
meant appertains. Just so it is with mean or common 
time. This is also a local reckoning, having for its epoch 
mean noon, or the average of all the times throughout the 
year, when the sun is on the meridian of that particular place 
to which it belongs ; and, therefore, in like manner, when we 
date any event by mean time, it is necessary to name the 
place, or particularize what mean time we intend. On the 
other hand, a date by equinoctial time is absolute, and re- 
quires no such explanatory addition. 

(253.) The astronomer sets and regulates his. sidereal 
clock by observing the meridian passages of the more con- 
spicuous and well-known stars. Each of these holds in the 
heavens a certain determinate and known place with respect 
to that imaginary point called the equinox, and by noting 
the times of their passage in succession by his clock he 
knows when the equinox passed. At that moment his 
clock ought to have marked h m s ; and if it did not, he 
knows and can correct its error, and by the agreement or 
disagreement of the errors assigned by each star he can as- 
certain whether his clock is correctly regulated to go twenty- 
four hours in one diurnal period, and if not, can ascertain 
and allow for its rate. Thus, although his clock may not, 
and indeed cannot, either be set correctly, or go truly, yet 



220 OUTLINES OF ASTRONOMY 

by applying its error and rate (as they are technically 
termed), he can correct its indications, and ascertain the 
exact sidereal times corresponding to them, and proper to 
his locality. This indispensable operation is called getting 
his local time. For simplicity of explanation, however, we 
shall suppose the clock a perfect instrument; or, which 
comes to the same thing, its error and rate applied at every 
moment it is consulted, and included in its indications. 

(254.) Suppose, now, of two observers, at distant sta- 
tions, A and B, each, independently of the other, to set 
and regulate his clock to the true sidereal time of his 
station. It is evident that if one of these clocks could be 
taken up without deranging its going, and set down by the 
side of the other, they would be found, on comparison, 
to differ by the exact difference of their local epochs; that 
is, by the time occupied by the equinox, or by any star, 
in passing from the meridian of A to that of B ; in other 
words, by their difference of longitude, expressed in sidereal 
hours, minutes, and seconds. 

(255.) A pendulum clock cannot be thus taken up and 
transported from place to place without derangement, but a 
chronometer may. Suppose, then, the observer at B to 
use a chronometer instead of a clock, he may, by bodily 
transfer of the instrument to the other station, procure a 
direct comparison of sidereal times, and thus obtain his 
longitude from A. And even if he employ a clock, yet 
by comparing it first with a good chronometer, and then 
transferring the latter instrument for comparison with the 
other clock, the same end will be accomplished, provided 
the going of the chronometer can be depended on. 

(256.) Were chronometers perfect, nothing more com- 
plete and convenient than this mode of ascertaining dif- 



OUTLINES OF ASTRONOMY 221 

ferences of longitude could be desired. An observer, 
provided with such an instrument, and with a portable 
transit, or some equivalent method of determining the 
local time at any given station, might, by journeying from 
place to place, and observing the meridian passages of 
stars at each (taking care not to alter his chronometer, 
or let it run down), ascertain their differences of longitude 
with any required precision. In this case, the same time- 
keeper being used at every station, if, at one of them, A, 
it mark true sidereal time, at any other, B, it will be just 
so much sidereal time in error as the difference of longi- 
tudes of A and B is equivalent to: in other words, the 
longitude of B from A will appear as the error of the time- 
keeper on the local time of B. If he travel westward, then 
his chronometer will appear continually to gain, although 
it really goes correctly. Suppose, for instance, he set out 
from A, when the equinox was on the meridian, or his 
chronometer at 11 , and in twenty-four hours (sid. time) had 
travelled 15° westward to B. At the moment of arrival 
there, his chronometer will again point to h ; but the 
equinox will be, not on his new meridian, but on that of 
A, and he must wait one hour more for its arrival at that 
of B. When it does arrive there, then his watch will point 
not to h but to l h , and will therefore be l h fast on the local 
time of B. If he travel eastward, the reverse will happen. 
(257.) Suppose an observer now to set out from any 
station as above described, and constantly travelling west- 
ward to make the tour of the globe, and return to the point 
he set out from. A singular consequence will happen; he 
will have lost a day in his reckoning of time. He will enter 
the day of his arrival in his diary, as Monday, for instance, 
when, in fact, it is Tuesday. The reason is obvious. Days 



222 OUTLINES OF ASTRONOMY 

and nights are caused by the alternate appearance of the 
sun and stars, as the rotation of the earth carries the spec- 
tator round to view them in succession. So many turns as 
he makes absolutely round the centre, so often will he pass 
through the earth's shadow, and emerge into light, and so 
many nights and days will he experience. But if he travel 
once round the globe in the direction of its motion, he will, 
on his arrival, have really made one turn more round its 
centre; and if in the opposite direction, one turn less than 
if he had remained upon one point of its surface: in the 
former case, then, he will have witnessed one alternation of 
day and night more, in the latter one less, than if he had 
trusted to the rotation of the earth alone to carry him round. 
As the earth revolves from west to east, it follows that a 
westward direction of his journey, by which he counteracts 
its rotation, will cause him to lose a day, and an eastward 
direction, by which he conspires with it, to gain one. In 
the former case, all his days will be longer; in the latter 
shorter than those of a stationary observer. This contin 
gency has actually happened to circumnavigators. Hence 
also, it must necessarily happen that distant settlements 
on the same meridian, will differ a day in their usual reck 
oning of time, according as they have been colonized by 
settlers arriving in an eastward or in a westward direction — 
a circumstance which may produce strange confusion when 
they come to communicate with each other. The only mode 
of correcting the ambiguity, and settling the disputes which 
such a difference may give rise to, consists in having re- 
course to the equinoctial date, which can never be am- 
biguous. 

(258.) Unfortunately for geography and navigation, the 
chronometer, though greatly and indeed wonderfully im- 



OUTLINES OF ASTRONOMY 223 

proved by the skill of modern artists, is yet far too imper- 
fect an instrument to be relied on implicitly. However such 
an instrument may preserve its uniformity of rate for a few 
hours, or even days, yet in long absences from home the 
chances of error and accident become so multiplied, as to 
destroy all security of reliance on even the best. To a 
certain extent this may, indeed, be remedied by carrying 
out several, and using them as checks on each other; but, 
besides the expense and trouble, this is only a palliation of 
the evil — the great and fundamental — as it is the only one 
to which the determination of longitudes by time-keepers is 
liable. It becomes necessary, therefore, to resort to other 
means of communicating from one station to another a 
knowledge of its local time, or of propagating from some 
principal station, as a centre, its local time as a universal 
standard with which the local time at any other, however 
situated, may be at once compared, and thus the longitudes 
of all places be referred to the meridian of such central 
point. 

(259.) The simplest and most accurate method by which 
this object can be accomplished, when circumstances admit 
of its adoption, is that by telegraphic signal. Let A and 
B be two observatories, or other stations, provided with 
accurate means of determining their respective local times, 
and let us first suppose them visible from each other. 
Their clocks being regulated, and their errors and rates 
ascertained and applied, let a signal be made at A, of some 
sudden and definite kind, such as the flash of gunpowder, 
the explosion of a rocket, the sudden extinction of a bright 
light, or any other which admits of no mistake, and can be 
seen at great distances. The moment of the signal being 
made must be noted by each observer at his respective clock 



224 OUTLINES OF ASTRONOMY 

or watch, as if it were the transit of a star, or any astro- 
nomical phenomenon, and the error and rate of the clock 
at each station being applied, the local time of the signal 
at each is determined. Consequently, when the observers 
communicate their observations of the signal to each other, 
since (owing to the almost instantaneous transmission of 
light) it must have been seen at the same absolute instant 
by both, the difference of their local times, and therefore 
of their longitudes, becomes known. For example, at A 
the signal is observed to happen at 5 h m s , sid. time at 
A, as obtained by applying the error and rate to the time 
shown by the clock at A, when the signal was seen there. 
At B the same signal was seen at 5 h 4 m s , sid. time, at B, 
similarly deduced from the time noted by the clock at B, by 
applying its error and rate. Consequently, the difference 
of their local epochs is 4 m s , which is also their differ- 
ence of longitudes in time, or 1° 0' 0* in hour angle. 

(260.) The accuracy of the final determination may be 
increased by making and observing several signals at stated 
intervals, each of which affords a comparison of times, and 
the mean of all which is, of course, more to be depended on 
than the result of any single comparison. By this means, 
the error introduced by the comparison of clocks may be 
regarded as altogether destroyed. 

(261.) The distances at which signals can be rendered 
visible must of course depend on the nature of the inter- 
posed country. Over sea the explosion of rockets may 
easily be seen at fifty or sixty miles ; and in mountainous 
countries the flash of gunpowder in an open spoon may be 
seen, if a proper station be chosen for its exhibition, at 
much greater distances. 

(262.) When the direct light of the flash can no longer be 



OUTLINES OF ASTRONOMY 225 

perceived, either owing to the convexity of the interposed 
segment of the earth, or to intervening obstacles, the sudden 
illumination cast on the under surface of the clouds by the 
explosion of considerable quantities of powder may often 
be observed with success; and in this way signals have been 
made at very much greater distances. Whatever means can 
be devised of exciting in two distant observers the same 
sensation, whether of sound, light, or visible motion, at 
precisely the same instant of time, may be employed as a 
longitude signal. Wherever, for instance, an unbroken line 
of electrotelegraphic connection has been, or hereafter may 
be, established, the means exist of making as complete a 
comparison of clocks or watches as if they stood side by 
side, so that no method more complete for the determina- 
tion of differences of longitude can be desired. Thus, the 
difference of longitude between the observatories of Green- 
wich and Paris was ascertained in 1854. The extreme de- 
viation of the most discordant result from the mean of 29 
single determinations (0 h. 9 m. 20 -64 sec), amounted barely 
to a quarter of a second. 

(263.) Where no such electric communication exists, 
however, the interval between observing stations may be 
increased by causing the signals to be made not at one of 
them, but at an intermediate point; for, provided they are 
seen by both parties; it is a matter of indifference where 
they are exhibited. Still the interval which could be thus 
embraced would be very limited, and the method in conse- 
quence of little use, but for the following ingenious con- 
trivance, by which it can be extended to any distance, 
and carried over any tract of country, however difficult. 

(264.) Tbis contrivance consists in establishing, between 
the extreme stations, whose difference of longitude is to be 



226 OUTLINES OF ASTRONOMY 

ascertained, and at which the local times are observed, a 
chain of intermediate stations, alternately destined for sig- 
nals and for observers. Thus, let A and Z be the extreme 
stations. At B let a signal station be established, at which 
rockets, etc., are fired at stated intervals. At let an 
observer be placed, provided with a chronometer; at D, 
another signal station; at E, another observer and chro- 
nometer; till the whole line is occupied by stations so 
arranged, that the signal at B can be seen from A and C ; 
those at D, from C and E ; and so on. Matters being thus 
arranged, and the errors and rates of the clocks at A and Z 
ascertained by astronomical observation, let a signal be 
made at B, and observed at A and C, and the times noted. 



I 



Thus the difference between A's clock and C's chronometer 
becomes known. After a short interval (five minutes for 
instance) let a signal be made at D, and observed by 
and E. Then will the difference between their respective 
chronometers be determined; and the difference between 
the former and the clock at A being already ascertained, 
the difference between the clock A and chronometer E is 
therefore known. This, however, supposes that the inter- 
mediate chronometer C has kept true sidereal time, or at 
least a known rate, in the interval between the signals 
Now this interval is purposely made so very short, that no 
instrument of any pretensions to character can possibly pro- 
duce an appreciable amount of error in its lapse by devia- 
tions from its usual rate. Thus the time propagated from 



OUTLINES OF ASTRONOMY 227 

A to C may be considered as handed over, without gain or 
loss (save from error of observation), to E. Similarly, by 
the signal made at F, and observed at E and Z, the time 
so transmitted to E is forwarded on to Z, and thus at length 
the clocks at A and Z are compared. The process may be 
repeated as often as is necessary to destroy error by a mean 
of results; and when the line of stations is numerous, by 
keeping up a succession of signals, so as to allow each 
observer to note alternately those on either side, which is 
easily prearranged, many comparisons may be kept running 
along the line at once, by which time is saved, and other 
advantages obtained. 15 In important cases the process is 
usually repeated on several nights in succession, 

(265.) In place of artificial signals, natural ones, when 
they occur sufficiently definite for observation, may be 
equally employed. In a clear night the number of those 
singular meteors, called shooting stars, which may be ob- 
served, is often very great, especially od the 9th and 10th 
of August, and some other days, as November 12 and 18; 
and as they are sudden in their appearance and disappear- 
ance, and from the great height at which they have been 
ascertained to take place are visible over extensive regions 
of the earth's surface, there is no doubt that they may be 
resorted to with advantage, by previous concert and agree- 
ment between distant observers to watch and note them. 16 



15 For a complete account of this method, and the mode of deducing the 
most advantageous result from a combination of all the observations, see a paper 
on the difference of longitudes of Greenwich and Paris, Phil, Trans. 1826, by 
the Author of this volume, 

16 This idea was first suggested by the late Dr. Maskelyne, to whom, how- 
ever, the practically useful fact of their periodic recurrence was unknown. Mr. 
Cooper has thus employed the meteors of the 10th and 12th August, 1847, to 
determine the difference of longitudes of Markree and Mount Eagle, in Ireland. 
Those of the same epoch have also been used in Germany for ascertaining the 
longitudes of several stations, and with very satisfactory results. 



228 OUTLINES OF ASTRONOMY 

Those sudden disturbances of the magnetic needle, to which 
the name of magnetic shocks has been given, have been sat- 
isfactorily ascertained to be, very often at least, simultane- 
ous over whole continents, and in some, perhaps, over the 
whole globe. These, if observed at magnetic observatories 
with precise attention to astronomical time, may become the 
means of determining their differences of longitude with 
more precision, possibly, than by any other method, if a 
sufficient number of remarkable shocks be observed to as- 
certain their identity, about which the intervals of time be- 
tween their occurrence (exactly alike at both stations) will 
leave no doubt. 

(266.) Another species of natural signal, visible at once 
over a whole terrestrial hemisphere, is afforded by the 
eclipses of Jupiter's satellites, of which we shall speak 
more at large when we come to treat of those bodies. 
Every such eclipse is an event which possesses one great 
advantage in its applicability to the purpose in question, 
viz. that the time of its happening, at any fixed station, 
such as Greenwich, can be predicted from a long course 
of previous recorded observation and calculation thereon 
founded, and that this prediction is sufficiently precise and 
certain, to stand in the place of a corresponding observa- 
tion. So that an observer at any other station wherever, 
who shall have observed one or more of these eclipses, and 
ascertained his local time, instead of waiting for a commu- 
nication with Greenwich, to inform him at what moment the 
eclipse took place there, may use the predicted Greenwich 
time instead, and thence, at once, and on the spot, deter- 
mine his longitude. This mode of ascertaining longitudes 
is, however, as will hereafter appear, not susceptible of 
great exactness, and should only be resorted to when others 



OUTLINES OF ASTRONOMY 229 

cannot be had. The nature of the observation also is such 
that it cannot be made at sea; 17 so that, however useful to 
the geographer, it is of no advantage to navigation. 

(267=) But such phenomena as these are of only occa- 
sional occurrence; and in their intervals, and when cut off 
from all communication with any fixed station, it is indis- 
pensable to possess some means of determining longitudes, 
on which not only the geographer may rely for a knowledge 
of the exact position of important stations on land in remote 
regions, but on which the navigator can securely stake, at 
every instant of his adventurous course, the lives of himself 
and comrades, the interests of his country, and the fortunes 
of his employers. Such a method is afforded by Lunar 
Observations. Though we have not yet introduced the 
reader to the phenomena of the moon's motion, this will 
not prevent us from giving here the exposition of the prin- 
ciple of the lunar method ; on the contrary, it will be highly 
advantageous to do so, since by this course we shall have to 
deal with the naked principle, apart from all the peculiar 
sources of difficulty with which the lunar theory is encum- 
bered, but which are, in fact, completely extraneous to the 
principle of its application to the problem of the longitudes, 
which is quite elementary. 

(268.) If there were in the heavens a clock furnished with 
a dial- plate and hands, which always marked Greenwich 



" To accomplish this is still a desideratum. Observing chairs, suspended 
with studious precaution for insuring freedom of motion, have been resorted 
to, under the vain hope of mitigating the effect of the ship's oscillation. The 
opposite course seems more promising, viz. to merely deaden the motion by 
a somewhat stiff suspension (as by a coarse and rough cable), and by friction 
strings attached to weights running through loops (not pulleys) fixed in the 
woodwork of the vessel. At least, such means have been found by the author 
of singular efficacy in increasing personal comfort in the suspension of a cot. 
[Vide Journal of the Society of Arts, January 4, 1861.] 



230 OUTLINES OF ASTRONOMY 

time, the longitude of any station would be at once deter- 
mined, so soon as the local lime was known, by comparing 
it with this clock. Now, the offices of the dial- plate and 
hands of a clock are these: — the former carries a set of 
marks upon it, whose position is known ; the latter, by 
passing over and among these marks, informs us, by the 
place it holds with respect to them, what it is o'clock, or 
what time has elapsed since a certain moment when it stood 
at one particular spot. 

(269.) In a clock the marks on the dial- plate are uni- 
formly distributed all around the circumference of a circle, 
whose centre is that on which the hands revolve with a uni- 
form motion. But it is clear that we should, with equal 
certainty, though with much more trouble, tell what o'clock 
it were, if the marks on the dial-plate were unequally dis- 
tributed — if the hands were eccentric, and their motion not 
uniform — provided we knew, 1st, the exact intervals round 
the circle at which the hour and minute marks were placed; 
which would be the case if we had them all registered in a 
table, from the results of previous careful measurement; — 
2dly, if we knew the exact amount and direction of excen- 
tricity of the centre of motion of the hands; — and, 3dly, if 
we were fully acquainted with all the mechanism which put 
the hands in motion, so as to be able to say at every instant 
what were their velocity of movement, and so as to be able 
to calculate, without fear of error, how much time should 
correspond to SO MUCH angular movement. 

(270.) The visible surface of the starry heavens is the 
dial- plate of our clock, the stars are the fixed marks dis- 
tributed around its circuit, the moon is the movable hand, 
which, with a motion that, superficially considered, seems 
uniform, but which, when carefully examined, is found to 



OUTLINES OF ASTRONOMY 231 

be far otherwise, and which, regulated by mechanical laws 
of astonishing complexity and intricacy in result, though 
beautifully simple in principle and design, performs a 
monthly circuit among them, passing visibly over and 
hiding, or, as it is called, occulting some, and gliding 
beside and between others; and whose position among 
them can, at any moment when it is visible, be exactly 
measured by the help of a sextant, just as we might meas- 
ure the place of our clock-hand among the marks on its 
dial -plate with a pair of compasses, and thence, from the 
known and calculated laws of its motion, deduce the time. 
That the moon does so move among the stars, while the lat- 
ter hold constantly, with respect to each other, the same 
relative position, the notice of a few nights, or even hours, 
will satisfy the commencing student, and this is all that at 
present we require. 

(271.) There is only one circumstance wanting to make 
our analogy complete. Suppose the hands of our clock, in- 
stead of moving quite close to the dial-plate, were consider- 
ably elevated above, or distant in front of it. Unless, then, 
in viewing it, we kept our eye just in the line of their cen- 
tre, we should not see them exactly thrown or projected upon 
their proper places on the dial. And if we were either un- 
aware of this cause of optical change of place, this parallax 
— or negligent in not taking it into account — we might make 
great mistakes in reading the time, by referring the hand to 
the wrong mark, or incorrectly appreciating its distance 
from the right. On the other hand, if we took care to note, 
in every case when we had occasion to observe the time, the 
exact position of the eye, there would be no difficulty in 
ascertaining and allowing for the precise influence of this 
cause of apparent displacement Now, this is just what 



232 OUTLINES OF ASTRONOMY 

obtains with the apparent motion of the moon among the 
stars. The former (as will appear) is comparatively near to 
the earth — the latter immensely distant; and in consequence 
of our not occupying the centre of the earth, but being car- 
ried about on its surface, and constantly changing place, 
there arises a parallax, which displaces the moon apparently 
among the stars, and must be allowed for before we can tell 
the true place she would occupy if seen from the centre. 

(272.) Such a clock as we have described might, no 
doubt, be considered a very bad one; but if it were our 
only one, and if incalculable interests were at stake on a 
perfect knowledge of time, we should justly regard it as 
most precious, and think no pains ill bestowed in studying 
the laws of its movements, or in facilitating the means of 
reading it correctly. Such, in the parallel we are drawing, 
is the lunar theory, whose object is to reduce to regularity 
the indications of this strangely irregular- going clock, to 
enable us to predict, long beforehand, and with absolute 
certainty, whereabouts among the stars, at every hour, min- 
ute, and second, in every day of every year, in Greenwich 
local time, the moon would be seen from the earth's centre, 
and will be seen from every accessible point of its surface; 
and such is the lunar method of longitudes. The moon's 
apparent angular distance from all those principal and con- 
spicuous stars which lie in its course, as seen from the 
earth's centre, are computed and tabulated with the utmost 
care and precision in almanacs published under national 
control. No sooner does an observer, in any part of the 
globe, at sea or on land, measure its actual distance from 
any one of those standard stars (whose places in the heavens 
have been ascertained for the purpose with the most anx- 
ious solicitude), than he has, in fact, performed that com- 



OUTLINES OF ASTRONOMY 233 

parison of his local time with the local times of every ob- 
servatory in the world, which enables him to ascertain his 
difference of longitude from one or all of them. 

(273.) The latitudes and longitudes of any number of 
points on the earth's surface may be ascertained by the 
methods above described; and by thus laying down a suffi- 
cient number of principal points, and filling in the inter- 
mediate spaces by local surveys, might maps of countries be 
constructed. In practice, however, it is found simpler and 
easier to divide each particular nation into a series of great 
triangles, the angles of which are stations conspicuously 
visible from each other. Of these triangles, the angles only 
are measured by means of the theodolite, with the exception 
of one side only of one triangle, which is called a base, and 
which is measured with every refinement which ingenuity 
can devise or expense command. This base is of moderate 
extent, rarely surpassing six or seven miles, and purposely 
selected in a perfectly horizontal plane, otherwise conven- 
iently adapted to the purposes of measurement. Its length 
between its two extreme points (which are dots on plates of 
gold or platina let into massive blocks of stone, and which 
are, or at least ought to be, in all cases preserved with almost 
religious care, as monumental records of the highest impor- 
tance), is then measured, with every precaution to insure 
precision, 18 and its position with respect to the meridian, as 
well as the geographical positions of its extremities, care- 
fully ascertained. 

(274.) The annexed figure represents such a chain of 
triangles. A B is the base, 0, C, stations visible from 



18 The greatest possible error in the Irish base of between seven and eight 
miles, near Londonderry, is supposed not to exceed two inches c 



234 OUTLINES OF ASTRONOMY 

both its extremities (one of which, 0, we will suppose to 
be a national observatory, with which it is a principal ob- 
ject that the base should be as closely and immediately 
connected as possible); and D, B, F, Gr, H, K, other sta- 
tions, remarkable points in the country, by whose connec- 
tion its whole surface may be covered, as it were, with a 
network of triangles. Now, it is evident that the angles 
of the triangle A, B, being observed, and one of its sides, 
A B, measured, the other two sides, A C, B C, may be 
calculated by the rules of trigonometry; and thus each of 




the sides A C and B C becomes in its turn a base capable 
of being employed as known sides of other triangles. For 
instance, the angles of the triangles ACG and B C F being 
known by observation, and their sides A G and B C, we 
can thence calculate the lengths A Gr, C Gr, and B F, C F, 
Again, C Gr and OF being known, and the included angle 
Gr F, Gr F may be calculated, and so on. Thus may all 
the stations be accurately determined and laid down, and 
as this process may be carried on to any extent, a map 
of the whole country may be thus constructed, and filled 
in to any degree of detail we please. 

(275.) Now, on this process there are two important re- 
marks to be made. The first is, that it is necessary to be 
careful in -the selection of stations, so as to form triangles 



OUTLINES OF ASTRONOMY 235 

free from any very great inequality in their angles. For 
instance, the triangle KBF would be a very improper one 
to determine the situation of F from observations at B and 
K, because the angle F being very acute, a small error in the 
angle K would produce a great one in the place of F upon 
the line B F. Such ill-conditioned triangles, therefore, must 
be avoided. But if this be attended to, the accuracy of the 
determination of the calculated sides will not be much short 
of that which would be obtained by actual measurement 
(were it practicable); and, therefore, as we recede from the 
base on all sides as a centre, it will speedily become prac- 
ticable to use as bases, the sides of much larger triangles, 
such as Gr F, Gr H, H K, etc. ; by which means the next 
step of the operation will come to be carried on on a much 
larger scale, and embrace far greater intervals, than it would 
have been safe to do (for the above reason) in the immediate 
neighborhood of the base. Thus it becomes easy to divide 
the whole face of a country into great triangles of from 30 
to 100 miles in their sides (according to the nature of the 
ground), which, being once well determined, may be after- 
ward, by a second series of subordinate operations, broken 
up into smaller ones, and these again into others of a still 
minuter order, till the final filling in is brought within the 
limits of personal survey and draughtsmanship, and till a 
map is constructed, with any required degree of detail. 

(276.) The next remark we have to make is, that all the 
triangles in question are not, rigorously speaking, plane, 
but spherical — existing on the surface of a sphere, or rather, 
to speak correctly, of an ellipsoid. In very small triangles 
of six or seven miles in the side, this may be neglected, as 
the difference is imperceptible; but in the larger ones it 
must be taken into consideration. It is evident that, as 



236 OUTLINES OF ASTRONOMY 

every object used for pointing the telescope of a theodolite 
has some certain elevation, not only above the soil, but above 
the level of the sea, and as, moreover, these elevations differ 
in every instance, a reduction to the horizon of all the meas- 
ured angles would appear to be required. But, in fact, by 
the construction of the theodolite (art. 192), which is noth- 
ing more than an altitude and azimuth instrument, this re- 
duction is made in the very act of reading off the horizontal 
angles. Let E be the centre of the earth; A, B, C, the 
places on its spherical surface, to which three stations, A, P, 
Q, in a country are referred by radii E A, E B P, E C Q. 
If a theodolite be stationed at A, the 
axis of its horizontal circle will point 
to E when truly adjusted, and its plane 
will be a tangent to the sphere at A, 
intersecting the radii E B P, E C Q, 
at M and N, above the spherical sur- 
face. The telescope of the theodolite, 
it is true, is pointed in succession to 
P, and Q; but the readings off of its 
azimuth circle give — not the angle 
P A Q between the directions of the telescope, or between 
the objects P, Q, as seen from A; but the azimuthal angle 
MAN, which is the measure of the angle A of the spherical 
triangle B A C. Hence arises this remarkable circumstance 
— that the sum of the three observed angles of any of the great 
triangles in geodesical operations is always found to be rather 
more than 180°. Were the earth's surface & plane, it ought to 
be exactly 180° ; and this excess, which is called the spherical 
excess, is so far from being a proof of incorrectness in the 
work, that it is essential to its accuracy, and offers at the 
same time another palpable proof of the earth's sphericity. 




OUTLINES OF ASTRONOMY 237 

(277.) The true way, then, of conceiving the subject of 
a trigonometrical survey, when the spherical form of the 
earth is taken into consideration, is to regard the network 
of triangles with which the country is covered, as the bases 
of an assemblage of pyramids converging to the centre of 
the earth. The theodolite gives us the true measures of the 
angles included by the planes of these pyramids; and the sur- 
face of an imaginary sphere on the level of the sea intersects 
them in an assemblage of spherical triangles; above whose 
angles, in the radii prolonged, the real stations of observa- 
tion are raised, by the superficial inequalities of mountain 
and valley. The operose calculations of spherical trigo- 
nometry which this consideration would seem to render nec- 
essary for the reductions of a survey, are dispensed with in 
practice by a very simple and easy rule, called the rule 
for the spherical excess, which is to be found in most works on 
trigonometry. If we would take into account the ellipticity 
of the earth, it may also be done by appropriate processes 
of calculation, which, however, are too abstruse to dwell 
upon in a work like the present. 

(278.) Whatever process of calculation we adopt, the 
result will be a reduction to the level of the sea, of 
all the triangles, and the consequent determination of 
the geographical latitude and longitude of every station 
observed. Thus we are at length enabled to construct 
maps of countries; to lay down the outlines of conti- 
nents and islands; the courses of rivers; the places of 
cities, towns and villages; the direction of mountain 
ridges, and the places of their principal summits; and all 
those details which, as they belong to physical and statis- 
tical, rather than to astronomical geography, we need not 
here dilate on. A few words, however, will be necessary 



238 OUTLINES OF ASTRONOMY 

respecting maps, which are used as well in astronomy as 
in geography. 

(279.) A map is nothing more than a representation, 
upon a plane, of some portion of the surface of a sphere, 
on which are traced the particulars intended to be expressed, 
whether they be continuous outlines or points. Now, as a 
spherical surface 19 can by no contrivance be extended or 
projected into a plane, without undue enlargement or con- 
traction of some parts in proportion to others ; and as the 
system adopted in so extending or projecting it will decide 
what parts shall be enlarged or relatively contracted, and 
in what proportions; it follows, that when large portions 
of the sphere are to be mapped down, a great difference in 
their representations may subsist, according to the system 
of projection adopted. 

(280.) The projections chiefly used in maps, are the 
orthographic, stereographic, and Mercator's. In the ortho- 
graphic projection, every point of the hemisphere is referred 
to its diametral plane or base, by a 
perpendicular let fall on it, so that the 
representation of the hemisphere thus 
mapped on its base, is such as would 
actually appear to an eye placed at 
an infinite distance from it. It is obvious, from the an- 
nexed figure, that in this projection only the central portions 
are represented of their true forms, while all the exterior is 
more and more distorted and crowded together as we ap- 
proach the edges of the map. Owing to this cause, the 
orthographic projection, though very good for small por- 
tions of the globe, is of little service for large ones. 

19 We here neglect the ellipticity of the earth, which, for such purpose as 
map-making, is too trifling to have any material influence. 




OUTLINES OF ASTRONOMY 



239 




(281.) The stereographic projection is in great measure 
free from this defect. To understand this projection we 
must conceive an eye to be placed at E, one extremity of 
a diameter, E C B, of the 
sphere, and to view the con- 
cave surface of the sphere, 
every point of which, as P, is 
referred to the diametral plane 
ADF, perpendicular to E B 
by the visual line P M E. The 
stereographic projection of a 
sphere, then, is a true perspec- 
tive representation of its con- 
cavity on a diametral plane; and, as such, it possesses 
some singularly elegant geometrical properties, of which 
we shall state one or two of the principal. 

(282.) And first, then, all circles on the sphere are rep- 
resented by circles in the projection. Thus the circle X is 
projected into x. Only great circles passing through the 
vertex B are projected into straight lines traversing the 
centre C: thus, B P A is projected into C A. 

2dly. Every very small triangle, Gr H K, on the sphere, 
is represented by a similar triangle g h k, in the projection. 
This is a very valuable property, as it insures a general 
similarity of appearance in the map to the reality in all its 
smaller parts, and enables us to project at least a hemi- 
sphere in a single map, without any violent distortion of 
the configurations on the surface from their real forms. As 
in the orthographic projection, the borders of the hemi- 
sphere are unduly crowded together; in the stereographic, 
their projected dimensions are, on the contrary, somewhat 
enlarged in receding from the centre. 



240 



OUTLINES OF ASTRONOMY 



(283.) Both these projections may be considered natural 
ones, inasmuch as they are really perspective representa- 
tions of the surface on a plane. Mercator's is entirely an 
artificial one, representing the sphere as it cannot be seen 
from any one point, but as it might be seen by an eye car- 
ried successively over every part of it. In it, the degrees 
of longitude, and those of latitude, bear always to each other 
their due proportion: the equator is conceived to be ex- 
tended out into a straight line, and the meridians are straight 
lines at right angles to it, as in the figure. Altogether, the 



















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general character of maps on this projection is not very 
dissimilar to what would be produced by referring every 
point in the globe to a circumscribing cylinder, by lines 
drawn from the centre, and then unrolling the cylinder into 
a plane. Like the stereographic projection, it gives a true 
representation, as to form, of every particular small part, 
but varies greatly in point of scale in its different regions; 
the polar portions in particular being extravagantly en- 
larged; and the whole map, even of a single hemisphere, 
not being comprisable within any finite limits. 

(283 a.) A very convenient projection, at once simple in 
principle, and remarkable for the facility with which places 
on the earth's surface may be laid down from a knowledge 
of their latitudes and longitudes, or stars from that of their 



OUTLINES OF ASTRONOMY 241 

right ascensions and polar distances; or read off from the 
chart when projected, is one in which (the radius of a circle 
being divided into ninety equal parts, representing degrees 
of polar distance) parallels of latitude or of declination are 
expressed by concentric circles, described through each of 
the points of division, and circles of longitude or of declina- 
tion are represented by the radii. In a planisphere con- 
structed on this principle, the proportions of the spaces 
occupied on the chart by equal areas differently situated, 
are better preserved than in any of those already described, 
and with an amount of distortion of shape, on the whole, as 
little offensive as the nature of a planisphere chart allows. 
This projection (as does also one recently proposed by Sir 
H. James, which takes in two-thirds of the sphere) admits 
of being extended considerably beyond a hemisphere, with- 
out producing a very intolerable distortion. 

(283 b.) The following projection, in which equal areas 
on the projection correspond precisely to equal areas on the 
spherical surface projected, is also occasionally employed. 20 

Take out, upon any scale, from a table of natural sines, 
the sines of 30', 1°, 1° 30', . . up to 45°, and from any centre 
with these as radii describe circles. These will represent 
the projections of small circles of the sphere about a pole, 
whose projection is their common centre, having the re- 
spective polar distances 1°, 2°, 3°, . . . 90°. 

(284.) "We shall not, of course, enter here into any geo- 
graphical details; but one result of maritime discovery on 
the great scale is, so to speak, massive enough to call for 
mention as an astronomical feature. When the continents 



20 See "Results of Astronomical Observations at the Cape of Good Hope," 
by the Author, Plate XL, where this projection is used to exhibit the law of 
distribution of the Nebulae. 

Astronomy— Vol. XIX— 11 



242 OUTLINES OF ASTRONOMY 

and seas are laid down on a globe (and since the discovery 
of Australia and -the recent addition to our antarctic knowl- 
edge of Victoria Land by Sir J. C. Ross, we are sure that 
no very extensive tracts of land remain unknown), we find 
that it is possible so to divide the globe into two hemi- 
spheres, that one shall contain nearly all the land', the other 
being almost entirely sea. It is a fact, not a little interest- 
ing to Englishmen, and, combined with our insular station 
in that great highway of nations, the Atlantic, not a little 
explanatory of our commercial eminence, that London 21 oc- 
cupies nearly the centre of the terrestrial hemisphere. As- 
tronomically speaking, the fact of this divisibility of the 
globe into an oceanic and a terrestrial hemisphere is impor- 
tant, as demonstrative of a want of absolute equality in the 
density of the solid material of the two hemispheres. Con- 
sidering the whole mass of land and water as in a state of 
equilibrium, it is evident that the half which protrudes must 
of necessity be buoyant] not, of course, that we mean to as- 
sert it to be lighter than water, but, as compared with the 
whole globe, in a less degree heavier than that fluid. We 
leave to geologists to draw from these premises their own 
conclusions (and we think them obvious enough) as to the 
internal constitution of the globe, and the immediate nature 
of the forces which, sustain its continents at their actual ele- 
vation; but in any future investigations which may have 
for their object to explain the local deviations of the inten- 



21 More exactly, Falmouth. The central point of the hemisphere which con- 
tains the maximum of land falls very nearly indeed upon this port. The land 
in the opposite hemisphere, with exception of the tapering extremity of South 
America and the slender peninsula of Malacca, is wholly insular, and were it 
not for Australia, would be quite insignificant in amount. This interesting 
feature of geography was first noticed by Colson (Phil. Tr. xxxix. p. 210). A 
pair of planispheres for the horizon of London has been published by Hughes 
(London 1839). 



OUTLINES OF ASTRONOMY 



243 



sity of gravity, from what the hypothesis of an exact elliptic 
figure would require, this, as a general fact, ought not to be 
lost sight of. 

(285. ) Our knowledge of the surface of our globe is in- 
complete, unless it include the heights above the sea level 
of every part of the land, and the depression of the bed of 
the ocean below the surface over all its extent. The latter 
object is attainable (with whatever difficulty and howsoever 
slowly) by direct sounding; the former by two distinct 
methods: the one consisting in trigonometrical measure- 
ment of the differences of level of all the stations of a sur- 
vey; the other, by the use of the barometer, the principle 
of which is, in fact, identical with that of the sounding line. 
In both cases we measure the distance of the point whose 
level we would know from the surface of an equilibrated 
ocean; only in the one case it is an ocean of water; in the 
other, of air. In the one case our sounding line is real and 
tangible; in the other, an imaginary one, measured by the 
length of the column of quicksilver the superincumbent air 
is capable of counterbalancing. 

(286.) Suppose that instead of air, the earth and ocean 
were covered with oil, and that human life could subsist 
under such circumstances. Let A B C D E be a continent, 




of which the portion ABC projects above the water, but is 
covered by the oil, which also floats at a uniform depth on 
the whole ocean. Then if we would know the depth of any 



244 OUTLINES OF ASTRONOMY 

point D below the sea level, we let down a plummet from F. 
But, if we would know the height of B above the same level, 
we have only to send up a float from B to the surface of the 
oil; and having done the same at G 1 a point at the sea level, 
the difference of the two float lines gives the height in question. 

(287.) Now, though the atmosphere differs from oil in 
not having a positive surface equally definite, and in not 
being capable of carrying up any float adequate to such a 
use, yet it possesses all the properties of a fluid really essen- 
tial to the purpose in view, and this in particular — that, 
over the whole surface of the globe, its strata of equal density 
supposed in a state of equilibrium, are parallel to the sur- 
face of equilibrium, or to what would be the surface of the 
sea, if prolonged under the continents, and therefore each or 
any of them has all the characters of a definite surface to 
measure from, provided it can be ascertained and identified. 
Now, the height at which, at any station B, the mercury in 
a barometer is supported, informs us at once how much of 
the atmosphere is incumbent on B, or, in other words, in 
what stratum of the general atmosphere (indicated by its 
density) B is situated: whence we are enabled finally to con- 
clude, by mechanical reasoning, 23 at what height above the 
sea level that degree of density is to be found over the whole 
surface of the globe. Such is the principle of the applica- 
tion of the barometer to the measurement of heights. For 
details, the reader is referred to other works. 23 

(288.) We will content ourselves here with a general 
caution against an implicit dependence on barometric meas- 

22 Newton's Princip. ii. Prop. 22. 

23 Biot, Astronomie Physique, vol. iii. For tables, see the work of Biot 
cited. Also those of Oltmann, annually published by the French board of longi- 
tudes in their Annuaire; and Mr. Baily's Collection of Astronomical Tables and 
Formulae. See also Encyc. Brit., "Meteorology," § 34. 



OUTLINES OF ASTRONOMY 245 

urements, except as a differential process, at stations not too 
remote from each other. They rely in their application on 
the assumption of a state of equilibrium in the atmospheric 
strata over the whole globe — which is very far from being 
their actual state (art. 37). "Winds, especially steady and 
general currents sweeping over extensive continents, un- 
doubtedly tend to produce some degree of conformity in 
the curvature of these strata to the general form of the land- 
surface, and therefore to give an undue elevation to the 
mercurial column at some points. On the other hand, the 
existence of localities on the earth's surface, where a per- 
manent depression of the barometer prevails to the astonish- 
ing extent of nearly an inch, has been clearly proved by the 
observations of Ermann in Siberia and of Eoss in the Ant- 
arctic Seas, and is probably a result of the same cause, and 
may be conceived as complementary to an undue habitual 
elevation in other regions. The mode in which both ele- 
vations and depressions of a permanent character may be 
maintained in the surface of a fluid in motion, will not be 
enigmatical to any one who contemplates the ripple caused 
by a pebble in a brook. 

(289.) Possessed of a knowledge of the heights of stations 
above the sea, we may connect all stations at the same alti- 
tude by level lines, the lowest of which will be the outline 
of the sea-coast; and the rest will mark out the successive 
coast- lines which would take place were the sea to rise by 
regular and equal accessions of level over the whole world, 
till the highest mountains were submerged. The bottoms 
of valleys and the ridge-lines of hills are determined by 
their property of intersecting all these level lines at right 
angles, and being, subject to that condition, the shortest 
and longest, that is to say, the steepest, and the most gently 



246 OUTLINES OF ASTRONOMY 

sloping courses respectively which can be pursued from the 
summit to the sea. The former constitute "the water 
courses" of a country; the latter its lines of "watershed" 24 
by which, it is divided into distinct basins of drainage. 
Thus originate natural districts of the most ineffaceable 
character, on which the distribution, limits, and peculiari- 
ties of human communities are in great measure dependent. 
The mean height of the continent of Europe, or that height 
which its surface would have were all inequalities levelled 
and the mountains spread equally over the plains, is, accord- 
ing to Humboldt, 1342 English feet; that of Asia, 2274; of 
North America, 1496; and of South America, 2302." 



CHAPTEK V 

OF URANOGRAPHY 

Construction of Celestial Maps and Globes by Observations of Right Ascen- 
sion and Declination — Celestial Objects Distinguished into Fixed and 
Erratic — Of the Constellations — Natural Regions in the Heavens — The 
Milky Way — The Zodiac — Of the Ecliptic — Celestial Latitudes and 
Longitudes — Precession of the Equinoxes — Nutation — Aberration — Re- 
fraction — Parallax — Summary View of the Uranographical Corrections 

(290.) The determination of the relative situations of 
objects in the heavens, and the construction of maps and 
globes which shall truly represent their mutual configura- 
tions as well as of catalogues which shall preserve a more 
precise numerical record of the position of each, is a task 
at once simpler and less laborious than that by which the 

24 Wasser-scheide, the separation of the waters. 

25 Humboldt's numbers are the halves of these, but express, not the mean 
heights of the surfaces, but the heights of the several centres of gravity of the 
continental masses above the sea level. 



OUTLINES OF ASTRONOMY 247 

surface of the earth is mapped and measured. Every star 
in the great constellation which appears to revolve above 
us, constitutes, so to speak, a celestial station; and among 
these stations we may, as upon the earth, triangulate, by 
measuring with proper instruments their angular distances 
from each other, which, cleared of the effect of refraction, 
are then in a state for laying down on charts, as we would 
the towns and villages of a country: and this without mov- 
ing from our place, at least for all the stars which rise above 
our horizon. 

(291.) Great exactness might, no doubt, be attained by 
this means, and excellent celestial charts constructed; but 
there is a far simpler and easier, and at the same time in- 
finitely more accurate course laid open to us if we take ad- 
vantage of the earth's rotation on its axis, and by observing 
each celestial object as it passes our meridian, refer it sepa- 
rately and independently to the celestial equator, and thus 
ascertain its place on the surface of an imaginary sphere, 
which may be conceived to revolve with it, and on which it 
may be considered as projected. 

(292.) The right ascension and declination of a point in 
the heavens correspond to the longitude and latitude of a 
station on the earth; and the place of a star on a celestial 
sphere is determined, when the former elements are known, 
just as that of a town on a map, by knowing the latter. 
The great advantages which the method of meridian obser- 
vation possesses over that of triangulation from star to star, 
are, then, 1st, That in it every star is observed in that point 
of its diurnal course, when it is best seen and least dis- 
placed by refraction. 2dly, That the instruments required 
(the transit and meridian circle) are the simplest and least 
liable to error or derangement of any used by astronomers. 



248 OUTLINES OF ASTRONOMY 

8dly, That all the observations can be made systematically, 
in regular succession, and with equal advantages; there 
being here no question about advantageous or disadvanta- 
geous triangles, etc. And, lastly, That, by adopting this 
course, the very quantities which we should otherwise have 
to calculate by long and tedious operations of spherical 
trigonometry, and which are essential to the formation of 
a catalogue, are made the objects of immediate measure- 
ment. It is almost needless to state, then, that this is the 
course adopted by astronomers. 

(293.) To determine the right ascension of a celestial 
object, all that is necessary is to observe the moment of 
its meridian passage with a transit instrument, by a clock 
regulated to exact sidereal time, or reduced to such by ap- 
plying its known error and rate. The rate may be obtained 
by repeated observations of the same star at its successive 
meridian passages. The error, however, requires a knowl- 
edge of the equinox, or initial point from which all right 
ascensions in the heavens reckon, as longitudes do on the 
earth from a first meridian. 

(294.) The nature of this point will be explained pres- 
ently; but for the purposes of uranography, in so far as 
they concern only the actual configurations of the stars 
inter se, a knowledge of the equinox is not necessary. The 
choice of the equinox, as a zero point of right ascensions, is 
purely artificial, and a matter of convenience. As on the 
earth, any station (as a national observatory) may be chosen 
for an origin of longitudes; so in uranography, any con- 
spicuous star might be selected as an initial point from 
which hour angles might be reckoned, and from which, by 
merely observing differences or intervals of time, the situa- 
tion of all others might be deduced. In practice, these in- 



OUTLINES OF ASTRONOMY 249 

tervals are affected by certain minute causes of inequality, 
which must be allowed for, and which will be explained 
in their proper places. 

(295.) The declinations of celestial objects are obtained, 
By observation of their meridian altitudes, with the mural 
or meridian circle, or other proper instruments. This re- 
quires a knowledge of the geographical latitude of the sta- 
tion of observation, which itself is only to be obtained by 
celestial observation. 2dly, And more directly, by observa- 
tion of their polar distances on the mural circle, as explained 
in art. 170, which is independent of any previous determi- 
nation of the latitude of the station; neither, however, in 
this case, does observation give directly and immediately 
the exact declinations. The observations require to be cor- 
rected, first for refraction, and moreover for those minute 
causes of inequality which have been just alluded to in the 
case of right ascensions. 

(296.) In this manner, then, may the places, one among 
the other, of all celestial objects be ascertained, and maps 
and globes constructed. Now here arises a very important 
question. How far are these places permanent ? Do these 
stars and the greater luminaries of heaven preserve forever 
one invariable connection and relation of place inter se, as 
if they formed part of a solid though invisible firmament; 
and, like the great natural landmarks on the earth, pre- 
serve immutably the same distances and bearings each from 
the other? If so, the most rational idea we could form 
of the universe would be that of an earth at absolute rest 
in the centre, and a hollow crystalline sphere circulating 
round it, and carrying sun, moon and stars along in its 
diurnal motion. If not, we must dismiss all such notions, 
and inquire individually into the distinct history of each 



250 OUTLINES OF ASTRONOMY 

object, with a view to discovering the laws of its peculiar 
motions, and whether any and what other connection sub- 
sists between them. 

(297o) So far is this, however, from being the case, that 
observations, even of the most cursory nature, are sufficient 
to show that some, at least, of the celestial bodies, and those 
the most conspicuous, are in a state of continual change of 
place among the rest. In the case of the moon, indeed, the 
change is so rapid and remarkable, that its alteration of 
situation with respect to such bright stars as may happen 
to # be near it may be noticed any fine night in a few hours ; 
and if noticed on two successive nights, cannot fail to strike 
the most careless observer. With the sun, too, the change 
of place among the stars is constant and rapid; though, 
from the invisibility of stars to the naked eye in the day- 
time, it is not so readily recognized, and requires either the 
use of telescopes and angular instruments to measure it, or 
a longer continuance of observation to be struck with it. 
Nevertheless, it is only necessary to call to mind its greater 
meridian altitude in summer than in winter, and the fact 
that the stars which come into view at night (and which 
are therefore situated in a hemisphere opposite to that oc- 
cupied by the sun, and having that luminary for its centre) 
vary with the season of the year, to perceive that a great 
change must have taken place in that interval in its relative 
situation with respect to all the stars. Besides the sun and 
moon, too, there are several other bodies, called planets, 
which, for the most part, appear to the naked eye only as 
the largest and most brilliant stars, and which offer the 
same phenomenon of a constant change of place among the 
stars; now approaching, and now receding from, such of 
them as we may refer them to as marks; and, some in 



OUTLINES OF ASTRONOMY 251 

longer, some in shorter periods, making, like the sun and 
moon, the complete tour of the heavens. 

(298.) These, however, are exceptions to the general 
rule. The innumerable multitude of the stars which are 
distributed over the vault of the heavens form a constel- 
lation, which preserves, not only to the eye of the casual 
observer, but to the nice examination of the astronomer, a 
uniformity of aspect which, when contrasted with the per- 
petual change in the configurations of the sun, moon and 
planets, may well be termed invariable. It is true, indeed, 
that, by the refinement of exact measurements prosecuted 
from age to age, some small changes of apparent place, at- 
tributable to no illusion and to no terrestrial cause, have 
been detected in many of them. Such are called, in as- 
tronomy, the proper motions of the stars. But these are 
so excessively slow, that their accumulated amount (even 
in those stars for which they are greatest) has been insuffi- 
cient, in the whole duration of astronomical history, to pro- 
duce any obvious or material alteration in the appearance 
of the starry heavens. 

(299.) This circumstance, then, establishes a broad dis- 
tinction of the heavenly bodies into two great classes; — 
the fixed, among which (unless in a course of observations 
continued for many years) no change of mutual situation 
can be detected; and the erratic, or wandering — (which is 
implied in the word planet 1 ) — including the sun, moon and 
planets, as well as the singular class of bodies termed com- 
ets, in whose apparent places among the stars, and among 
each other, the observation of a few days, or even hours, 
is sufficient to exhibit an indisputable alteration. 

i nxavTjTTjs, a wanderer. 



252 OUTLINES OF ASTRONOMY 

(300.) Uranography, then, as it concerns the fixed celes- 
tial bodies (or, as they are usually called, the fixed stars), 
is reduced to a simple marking down of their relative places 
on a globe or on maps; to the insertion on that globe, in 
its due place in the great constellation of the stars, of the 
pole of the heavens, or the vanishing point of parallels to 
the earth's axis; and of the equator and place of the equi- 
nox: points and circles these, which, though artificial and 
having reference entirely to our earth, and therefore subject 
to all changes (if any) to which the earth's axis may be lia- 
ble, are yet so convenient in practice, that they have ob- 
tained an admission (with some other circles and lines), 
sanctioned by usage, in all globes and planispheres. The 
reader, however, will take care to keep them separate in his 
mind, and to familiarize himself with the idea rather of two 
or more celestial globes, superposed and fitting on each 
other, on one of which — a real one — are inscribed the stars; 
on the others those imaginary points, lines and circles, 
which astronomers have devised for their own uses, and 
to aid their calculations; and to accustom himself to con- 
ceive in the latter or artificial spheres a capability of being 
shifted in any manner upon the surface of the other; so 
that, should experience demonstrate (as it does) that these 
artificial points and lines are brought, by a slow motion of 
the earth's axis, or by other secular variations (as they are 
called), to coincide, at very distant intervals of time, with 
"different stars, he may not be unprepared for the change, 
and may have no confusion to correct in his notions. 

(301.) Of course we do not here speak of those uncouth 
figures and outlines of men and monsters, which are usually 
scribbled over celestial globes and maps, and serve, in a 
rude and barbarous way, to enable us to talk of groups of 



OUTLINES OF ASTRONOMY 253 

stars, or districts in the heavens, by names which, though 
absurd or puerile in their origin, have obtained a currency 
from which it would be difficult to dislodge them. In so 
far as they have really (as some have) any slight resem- 
blance to the figures called up in imagination by a view 
of the more splendid "constellations," they have a certain 
convenience; but as they are otherwise entirely arbitrary, 
and correspond to no natural subdivisions or groupings 
of the stars, astronomers treat them lightly, or altogether 
disregard them 2 except for briefly naming remarkable stars, 
as a Leonis, /? Scorpii, etc., by letters of the Greek alphabet 
attached to them. The reader will find them on any celes- 
tial charts or globes, and may compare them with the 
heavens, and there learn for himself their position. 

(302.) There are not wanting, however, natural districts 
in the heavens, which offer great peculiarities of character, 
and strike every observer: such is the milky way, that great 
luminous band, which stretches, every evening, all across 
the sky, from horizon to horizon, and which, when traced 
with diligence, and mapped down, is found to form a zone 
completely encircling the whole sphere, almost in a great 
circle, which is neither an hour circle, nor coincident with 
any other of our astronomical grammata. It is divided in 
one part of its course, sending off a kind of branch, which 
unites again with the main body, after remaining distinct 
for about 150 degrees, within which it suffers an interrup- 
tion in its continuity. This remarkable belt has main- 

2 This disregard is neither supercilious nor causeless. The constellations 
seem to have been almost purposely named and delineated to cause as much 
confusion and inconvenience as possible. Innumerable snakes twine through 
long and contorted areas of the heavens, where no memory can follow them; 
bears, lions and fishes, large and small, northern and southern, confuse all no- 
menclature, etc. A better system of constellations might have been a material 
help as an artificial memory. 



254 OUTLINES OF ASTRONOMY 

tained, from the earliest ages, the same relative situation 
among the stars, and, when examined through powerful 
telescopes, is found (wonderful to relate !) to consist entirely 
of stars scattered by millions, like glittering dust, on the 
black ground of the general heavens. It will be described 
more particularly in the subsequent portion of this work. 
(303.) Another remarkable region in the heavens is the 
zodiac, not from anything peculiar in its own constitution, 
but from its being the area within which the apparent mo- 
tions of the sun, moon, and all the greater planets are con- 
fined. To trace the path of any one of these, it is only 
necessary to ascertain, by continued observation, its places 
at successive epochs, and entering these upon our map or 
sphere in sufficient number to form a series, not too far 
disjoined, to connect them by lines from point to point, as 
we mark out the course of a vessel at sea by mapping down 
its place from day to day. Now when this is done, it is 
found, first, that the apparent path, or track, of the sun on 
the surface of the heavens, is no other than an exact great 
circle of the sphere which is called the ecliptic, and which is 
inclined to the equinoctial at an angle of about 23° 28', 
intersecting it at two opposite points, called the equinoctial 
points, or equinoxes, and which are distinguished from each 
other by the epithets vernal and autumnal; the vernal being 
that at which the sun crosses the equinoctial from south to 
north ; the autumnal, when it quits the northern and enters 
the southern hemisphere. Secondly, that the moon and all 
the planets pursue paths which, in like manner, encircle the 
whole heavens, but are not, like that of the sun, great 
circles exactly returning into themselves and bisecting the 
sphere, but rather spiral curves of much complexity, and 
described with very unequal velocities in their different 



OUTLINES OF ASTRONOMY 255 

parts. They have all, however, this in common, that the 
general direction of their motions is the same with that of 
the sun, viz. from west to east, that is to say, the contrary 
to that in which both they and the stars appear to be carried 
by the diurnal motion of the heavens; and, moreover, that 
they never deviate far from the ecliptic on either side, cross- 
ing and recrossing it at regular and equal intervals of time, 
and confining themselves within a zone, or belt (the zodiac 
already spoken of), extending (with certain exceptions among 
the smaller planets) not further than 8° or 9° on either side 
of the ecliptic. 

(304.) It would manifestly be useless to map down on 
globes or charts the apparent paths of any of those bodies 
which never retrace the same course, and which, therefore, 
demonstrably, must occupy at some one moment or other 
of their history, every point in the area of that zone of the 
heavens within which they are circumscribed. The ap- 
parent complication of their movements arises (that of the 
moon excepted) from our viewing them from a station 
which is itself in motion, and would disappear, could we 
shift our point of view and observe them from the sun. On 
the other hand the apparent motion of the sun is presented 
to us under its least involved form, and is studied, from 
the station we occupy, to the greatest advantage. So that, 
independent of the importance of that luminary to us in 
other respects, it is by the investigation of the laws of its 
motions in the first instance that we must rise to a knowl- 
edge of those of all the other bodies of our system. 

(305.) The ecliptic, which is its apparent path among 
the stars, is traversed by it in the period called the sidereal 
year, which consists of 365 d 6 h 9 m 9 -6 s , reckoned in mean 
solar time, or 366 d 6 h 9 m 9 -6 s , reckoned in sidereal time. The 



256 OUTLINES OF ASTRONOMY 

reason of this difference (and it is this which constitutes 
the origin of the difference between solar and sidereal time) 
is, that as the sun's apparent annual motion among the stars 
is performed in a contrary direction to the apparent diurnal 
motion of both sun and stars, it comes to the same thing as 
if the diurnal motion of the sun were so much slower than 
that of the stars, or as if the sun lagged behind them in its 
daily course. When this has gone on for a whole year, the 
sun will have fallen behind the stars by a whole circum- 
ference of the heavens — or, in other words, in a year the 
sun will have made fewer diurnal revolutions, by one, than 
the stars. So that the same interval of time which is meas- 
ured by 366 d 6 b , etc. , of sidereal time, will be called 365 days, 
6 hours, etc. , if reckoned in mean solar time. Thus, then, 
is the proportion between the mean solar and sidereal day 
established, which, reduced into a decimal fraction, is that 
of 1-00273791 to 1. The measurement of time by these 
different standards may be compared to that of space by 
the standard feet, or ells of two different nations; the pro- 
portion of which, once settled and borne in mind, can never 
become a source of error. 

(306.) The position of the ecliptic among the stars may, 
for our present purpose, be regarded as invariable. It is 
true that this is not strictly the case; and on comparing 
together its position at present with that which it held at 
the most distant epoch at which we possess observations, 
we find evidences of a small change, which theory accounts 
for, and whose nature will be hereafter explained: but that 
change is so excessively slow, that for a great many succes- 
sive years, or even for whole centuries, this circle may be 
regarded, for most ordinary purposes, as holding the same 
position in the sidereal heavens. 



OUTLINES OF ASTRONOMY 257 

(307.) The poles of the ecliptic, like those of any other 
great circle of the sphere, are opposite points on its surface, 
equidistant from the ecliptic in every direction. They are 
of course not coincident with those of the equinoctial, but 
removed from it by an angular interval equal to the inclina- 
tion of the ecliptic to the equinoctial (23° 28'), which is 
called the obliquity of the ecliptic. In the next figure, if 
P p represent the north and south poles (by which when 
used without qualification we always mean the poles of the 
equinoctial), and E A Q Y the equinoctial, VSAW the 
ecliptic, and K h, its poles — the spherical angle Q V S is 
the obliquity of the ecliptic, and is equal in angular meas- 
ure to P K or S Q. If we suppose the sun's apparent mo- 
tion to be in the direction V S A "W, Y will be the vernal 
and A the autumnal equinox. S and W, the two points at 
which the ecliptic is most distant from the equinoctial, are 
termed solstices, because, when arrived there, the sun ceases 
to recede from the equator, and (in that sense, so far as its 
motion in declination is concerned) to stand still in the 
heavens. S, the point where the sun has the greatest 
northern declination, is called the summer, and "W, that 
where it is furthest south, the winter solstice. These epi- 
thets obviously have their origin in the dependence of the 
seasons on the sun's declination, which will be explained 
in the next chapter. The circle E EPQ^, which passes 
through the poles of the ecliptic and equinoctial, is called 
the solstitial colure; and a meridian drawn through the 
equinoxes, P Y p A, the equinoctial colure. 

(308.) Since the ecliptic holds a determinate situation in 
the starry heavens, it may be employed, like the equinoc- 
tial, to refer the positions of the stars to, by circles drawn 
through them from its poles, and therefore, perpendicular 



258 



OUTLINES OF ASTRONOMY 




to it. Such circles are termed, in astronomy, circles of 
latitude — the distance of a star from the ecliptic, reckoned 
on the circle of latitude passing through it, is called the 
latitude of the stars — and the arc of the ecliptic intercepted 
between the vernal equinox and this circle, its longitude. In 

the figure, X is a star, PXRa cir- 
cle of declination drawn through 
it, by which it is referred to the 
equinoctial, and K X T a circle 
of latitude referring it to the 
ecliptic — then, as Y E is the right 
ascension, and E X the declina- 
tion, of X, so also is Y T its 
longitude, and T X its latitude. 
The use of the terms longitude 
and latitude, in this sense, seems to have originated in 
considering the ecliptic as forming a kind of natural 
equator to the heavens, as the terrestrial equator does 
to the earth — the former holding an invariable position 
with respect to the stars, as the latter does with respect 
to stations on the earth's surface. The force of this ob- 
servation will presently become apparent. 

(309.) Knowing the right ascension and declination of an 
object, we may find its longitude and latitude, and vice 
versa. This is a problem of great use in physical astronomy 
— the following is its solution: In our last figure, E K P Q, 
the solstitial colure is of course 90° distant from Y, the 
vernal equinox, which is one of its poles — so that Y E (the 
right ascension) being given, and also Y B, the arc E E, 
and its measure, the spherical angle E P E, or K P X, is 
known. In the spherical triangle K P X, then, we have 
given, 1st, the side P K, which, being the distance of the 



OUTLINES OF ASTRONOMY 



259 



poles of the ecliptic and equinoctial, is equal to the ob- 
liquity of the ecliptic; 2, the side P X, the polar dis- 
tance, or the complement of the declination R X; and, 3, 
the included angle K P X; and therefore, by spherical 
trigonometry, it is easy to find the other side K X, and 
the remaining angles. Now K X is the complement of the 
required latitude X T, and the angle P K X being known, 
and P K V being a right angle (because S Y is 90°), the 
angle X K Y becomes known. Now this is no other than 
the measure of the longitude Y T of the object. The in- 
verse problem is resolved by the same triangle, and by a 
process exactly similar. 

(310.) It is often of use to know the situation of the 
ecliptic in the visible heavens at any instant; that is to 
say, the points where it cuts the horizon, and the altitude 
of its highest point, or, as it is sometimes called, the 
nonagesimal point of the ecliptic, as well as the longitude 
of this point on the ecliptic itself 
from the equinox. These, and all 
questions referable to the same data 
and qusesita, are resolved by the 
spherical triangle Z P E, formed 
by the zenith Z (considered as the 
pole of the horizon), the pole of 
the equinoctial P, and the pole of 
the ecliptic E. The sidereal time 
being given, and also the right ascension of the pole of the 
ecliptic (which is always the same, viz. 18 h m s ), the hour 
angle Z P E of that point is known. Then, in this tri- 
angle we have given P Z, the co-latitude; P E, the polar 
distance of the pole of the ecliptic, 23° 28', and the angle 
Z P E from which we may find, 1st, the side Z E, which is 




260 OUTLINES OF ASTRONOMY 

easily seen to be equal to the altitude of the nonagesimal 
point sought; and 2dly, the angle P Z E, which is the azi- 
muth of the pole of the ecliptic, and which f therefore, being 
added to and subtracted from 90°, gives the azimuth of 
the eastern and western intersections of the ecliptic with 
the horizon. Lastly, the longitude of the nonagesimal 
point may be had, by calculating in the same triangle the 
angle P E Z, which is its complement 

(311.) The angle of situation of a star is the angle in- 
cluded between circles of latitude and of declination pass- 
ing through it. To determine it in any proposed case, we 
must resolve the triangle P S E, in which are given P S, 
P E, and the angle S P E, which is the difference between 
the star's right ascension and 18 hours; from which it is 
easy to find the angle P S E required- This angle is of use 
in many inquiries in physical astronomy. It is called in 
most books on astronomy, the angle of position, but this 
expression has become otherwise aod more conveniently 
appropriated. (See art. 204.) 

(312.) The same course of observations by which the 
path of the sun among the fixed stars is traced, and the 
ecliptic marked out among them, determines, of course, the 
place of the equinox Y (fig. art. 308) ppon the starry sphere, 
at that time — a point of great importance in practical astron- 
omy, as it is the origin or zero point of right ascension. 
Now, when this process is repeated at considerably distant 
intervals of time, a very remarkable phenomenon is ob- 
served; viz. that the equinox does not preserve a constant 
place among the stars, but shifts its position, travelling con- 
tinually and regularly, although with extreme slowness, 
backward, along the ecliptic, in the direction Y W from east 
to west, or the contrary to that in which the sun appears to 



OUTLINES OF ASTRONOMY 261 

move in that circle. As the ecliptic and equinoctial are not 
very much inclined, this motion of the equinox from east 
to west along the former, conspires (speaking generally) with 
the diurnal motion, and carries it, with reference to that mo- 
tion, continually in advance upon the stars: hence it has ac- 
quired the name of the precession of the equinoxes, because the 
place of the equinox among the stars, at every subsequent 
moment, precedes (with reference to the diurnal motion) that 
which it held the moment before. The amount of this mo- 
tion by which the equinox travels backward, or retrogrades 
(as it is called), on the ecliptic, is 0° 0' 50-10" per annum, an 
extremely minute quantity, but which, by its continual 
accumulation from year to year, at last makes itself very 
palpable, and that in a way highly inconvenient to practical 
astronomers, by destroying, in the lapse of a moderate num- 
ber of years, the arrangement of their catalogues of stars, 
and making it necessary to reconstruct them. Since the 
formation of the earliest catalogue on record, the place of 
the equinox has retrograded already about 30°. The period 
in which it performs a complete tour of the ecliptic is 25,868 
years. 

(313.) The immediate uranographical effect of the pre- 
cession of the equinoxes is to produce a uniform increase of 
longitude in all the heavenly bodies, whether fixed or er- 
ratic. For the vernal equinox being the initial point of 
longitudes, as well as of right ascension, a retreat of this 
point on the ecliptic tells upon the longitudes of all alike, 
whether at rest or in motion, and produces, so far as its 
amount extends, the appearance of a motion in longitude 
common to all, as if the whole heavens had a slow rotation 
round the poles of the ecliptic in the long period above 
mentioned, similar to what they have in twenty-four hours 



262 OUTLINES OF ASTRONOMY 

round those of the equinoctial. This increase of longitude, 
the reader will of course observe and bear in mind, is, prop- 
erly speaking, neither a real nor an apparent movement of 
the stars. It is a purely technical result, arising from the 
gradual shifting of the zero point from which longitudes are 
reckoned. Had a fixed star been chosen as the origin of 
longitudes, they would have been invariable. 

(314.) To form a just idea of this curious astronomical 
phenomenon, however, we must abandon, for a time, the 
consideration of the ecliptic, as tending to produce confu- 
sion in our ideas; for this reason, that the stability of the 
ecliptic itself among the stars is (as already hinted, art. 306) 
only approximate, and that in consequence its intersection 
with the equinoctial is liable to a certain amount of change, 
arising from its fluctuation, which mixes itself with what is 
due to the principal uranographical cause of the phenome- 
non. This cause will become at once apparent, if, instead 
of regarding the equinox, we fix our attention on the pole 
of the equinoctial, or the vanishing point of the earth's axis. 

(315.) The place of this point among the stars is easily 
determined at any epoch, by the most direct of all astronom- 
ical observations — those with the meridian or mural circle. 
By this instrument we are enabled to ascertain at every 
moment the exact distance of the polar point from any three 
or more stars, and therefore to lay it down, by triangulating 
from these stars, with unerring precision, on a chart or 
globe, without the least reference to the position of the 
ecliptic, or to any other circle not naturally connected with 
it. Now, when this is done with proper diligence and ex- 
actness, it results that, although for short intervals of time, 
such as a few days, the place of the pole may be regarded as 
not sensibly variable, yet in reality it is in a state of con- 



OUTLINES OF ASTRONOMY 263 

stant, al though extremely slow motion; and, what is still 
more remarkable, this motion is not uniform, but com- 
pounded of one principal, uniform, or nearly uniform, part, 
and other smaller and subordinate periodical fluctuations: 
the former giving rise to the phenomena of precession ; the 
latter to another distinct phenomenon called nutation. 
These two phenomena, it is true, belong, theoretically 
speaking, to one and the same general head, and are inti- 
mately connected together, forming part of a great and com- 
plicated chain of consequences flowing from the earth's rota- 
tion on its axis: but it will be conducive to clearness at 
present to consider them separately. 

(316.) It is found, then, that in virtue of the uniform 
part of the motion of the pole, it describes a circle in the 
heavens around the pole of the ecliptic as a centre, keeping 
constantly at the same distance of 23° 28' from it in a direc- 
tion from east to west, and with such a velocity, that the 
annual angle described by it, in this its imaginary orbit, is 
50 -10" ; so that the whole circle would be described by it in 
the above-mentioned period of 25,868 years. It is easy to 
perceive how such a motion of the pole will give rise to the 
retrograde motion of the equinoxes ; for in the figure, art. 
308, suppose the pole P in the progress of its motion in the 
small circle P O Z round K to come to O, then, as the situa- 
tion of the equinoctial E Y Q is determined by that of the 
pole, this, it is evident, must cause a displacement of the 
equinoctial, which will take a new situation, E U Q, 90° 
distant in every part from the new position O of the pole. 
The point IT, therefore, in which the displaced equinoctial 
will intersect the ecliptic, i.e. the displaced equinox, will 
lie on that side of V, its original position, toward which the 
motion of the pole is directed, or to the westward. 



264 OUTLINES OF ASTRONOMY 

(317.) The precession of the equinoxes thus conceived, 
consists, then, in a real but very slow motion of the pole of 
the heavens among the stars, in a small circle round the pole 
of the ecliptic. Now this cannot happen without producing 
corresponding changes in the apparent diurnal motion of the 
sphere, and the aspect which the heavens must present at 
very remote periods of history. The pole is nothing more 
than the vanishing point of the earth's axis. As this point, 
then, has such a motion as we have described, it necessarily 
follows that the earth's axis must have a conical motion, in 
virtue of which it points successively to every part of the 
small circle in question. We may form the best idea of 
such a motion by noticing a child's pegtop, when it spins 
not upright, or that amusing toy the te- to- turn, which, when 
delicately executed, and nicely balanced, becomes an ele- 
gant philosophical instrument, and exhibits, in the most 
beautiful manner, the whole phenomenon. The reader will 
take care not to confound the variation of the position of the 
earth's axis in space with a mere shifting of the imaginary 
line about which it revolves, in its interior. The whole 
earth participates in the motion, and goes along with the 
axis as if it were really a bar of iron driven through it. 
That such is the case is proved by the two great facts: 
1st, that the latitudes of places on the earth, or their geo- 
graphical situation with respect to the poles, have under- 
gone no perceptible change from the earliest ages. 2dly, 
that the sea maintains its level, which could not be the case 
if the motion of the axis were not accompanied with a mo- 
tion of the whole mass of the earth. s 



3 Local changes of the sea level, arising from purely geological causes, 
are easily distinguished from that general and systematic alteration which a 
shifting of the axis of rotation would give rise to. 



OUTLINES OF ASTRONOMY 265 

(318.) The visible effect of precession on the aspect of 
the heavens consists in the apparent approach of some stars 
and constellations to the pole and recess of others. The 
bright star of the Lesser Bear, which we call the pole star, 
has not always been, nor will always continue to be, our 
cynosure. At the time of the construction of the earliest 
catalogues it was 12° from the pole — it is now only 1° 24', 
and will approach yet nearer, to within half a degree, after 
which it will again recede, and slowly give place to others, 
which will succeed in its companionship to the pole. After 
a lapse of about 12,000 years, the. star a Lyras, the brightest 
in the northern hemisphere, will occupy the remarkable 
situation of a pole star approaching within about 5° of 
the pole. 

(319.) At the date of the erection of the Great Pyramid 
of Gizeh, which precedes by 3970 years (say 4000) the pres- 
ent epoch, the longitudes of all the stars were less by 55° 45' 
than at present. Calculating from this datum 4 the place of 
the pole of the heavens among the stars, it will be found to 
fall near a Draconis; its distance from that star being 
3° 44' 25". This being the most conspicuous star 6 in the 
immediate neighborhood was therefore the pole star at that 
epoch. And the latitude of Grizeh being just 30° north, and 
consequently the altitude of the north pole there also 30°, it 
follows that the star in question must have had at its lower 
culmination, at Grizeh, an altitude of 26° 15' 35". Now it is 
a remarkable fact, ascertained by the late researches of Col. 



4 On this calculation the diminution of the obliquity of the ecliptic in the 
4000 years elapsed has no influence. That diminution arises from a change in 
the plane of the earth's orbit, and has nothing to do with the change in the 
position of its axis, as referred to the starry sphere, 

5 a Draconis is now an inconspicuous star of the 4th magnitude, but there 
is distinct evidence to show that it was formerly brighter. 

Astronomy — Vol. XIX — 12 



266 OUTLINES OF ASTRONOMY 

Vyse, that of the nine pyramids still existing at Grizeh, six 
(including all the largest) have the narrow passages by 
which alone they can be entered (all which open out on the 
northern faces of their respective pyramids) inclined to the 
horizon downward at angles as follows: 

1st, or Pyramid of Cheops 26° 41' 

2d, or Pyramid of Cephren 25 55 

3d, or Pyramid of Mycerinus 26 2 

4th, 27 

5th, . . . 27 12 

9th, 28 . 

Mean . 26 47 

Of the two pyramids at Abousseir also, which alone 
exist in a state of sufficient preservation to admit of the in- 
clinations of their entrance passages being determined, one 
has_ the angle 27° 5', the other 26°. 

(320.) At the bottom of every one of these passages, 
therefore, the then pole star must have been visible at its 
lower culmination, a circumstance which can hardly be sup- 
posed to have been unintentional, and was doubtless con- 
nected (perhaps superstitiously) with the astronomical obser- 
vation of that star, of whose proximity to the pole at the 
epoch of the erection of these wonderful structures, we are 
thus furnished with a monumental record of the most im- 
perishable nature. 

(321.) The nutation of the earth's axis is a small and slow 
subordinate gyratory movement, by which, if subsisting 
alone, the pole would describe among the stars, in a period 
of about nineteen years, a minute ellipsis, having its longer 
axis equal to 18" -5, and its shorter to 13" -74; the longer 
being directed toward the pole of the ecliptic, and the 
shorter, of course, at right angles to it. The consequence 
of this real motion of the pole is an apparent approach and 



OUTLINES OF ASTRONOMY 267 

recess of all the stars in the heavens to the pole in the same 
period. Since, also, the place of the equinox on the ecliptic 
is determined by the place of the pole in the heavens, the 
same cause will give rise to a small alternate advance and 
recess of the equinoctial points, by which, in the same 
period, both the longitudes and the right ascensions of the 
stars will be also alternately increased and diminished. 

(322.) Both these motions, however, although here con- 
sidered separately, subsist jointly; and since, while in virtue 
of the nutation, the pole is describing its little ellipse of 
18" *5 in diameter, it is carried by the greater and regularly 
progressive motion of precession over so much of its circle 
round the pole of the ecliptic as corresponds to nineteen 
years — that is to say, over an angle of nineteen times 50" -1 
round the centre (which, in a small circle of 23° 28' in 
diameter, corresponds to 6' 20", as seen from the centre of 
the sphere): the path which it will pursue in virtue of the 
two motions, subsisting jointly, will be neither an ellipse 
nor an exact circle, but a gently undulated ring like that 
in the figure (where, however, the undulations are much 
exaggerated). (See fig. to art. 325.) 

(323.) These movements of precession and nutation are 
common to all the celestial bodies, both fixed and erratic; 
and this circumstance makes it impossible to attribute them 
to any other cause than a real motion of the earth's axis 
such as we have described. Did they only affect the stars, 
they might, with equal plausibility, be urged to arise from a 
real rotation of the starry heavens, as a solid shell, round an 
axis passing through the poles of the ecliptic in 25,868 
years, and a real elliptic gyration of that axis in nineteen 
years : but since they also affect the sun, moon, and planets, 
which, having motions independent of the general body of 



268 OUTLINES OF ASTRONOMY 

the stars, cannot without extravagance be supposed attached 
to the celestial concave, 6 this idea falls to the ground; and 
there only remains, then, a -real motion in the earth by 
which they can be accounted for. It will be shown in a 
subsequent chapter that they are necessary consequences of 
the rotation of the earth, combined with its elliptical figure, 
and the unequal attraction of the sun and moon on its polar 
and equatorial regions. 

(324.) Uranographically considered, as affecting the ap- 
parent places of the stars, they are of the utmost importance 
in practical astronomy. When we speak of the right ascen- 
sion and declination of a celestial object, it becomes neces- 
sary to state what epoch we intend, and whether we mean 
the mean right ascension — cleared, that is, of the periodical 
fluctuation in its amount, which arises from nutation, or the 
apparent right ascension, which, being reckoned from the 
actual place of the vernal equinox, is affected by the period- 
ical advance and recess of the equinoctial point produced 
by nutation — and so of the other elements. It is the prac- 
tice of astronomers to reduce, as it is termed, all their obser- 
vations, both of right ascension and declination, to some 
common and convenient epoch — such as the beginning of 
the year for temporary purposes, or of the decade, or the 
century for more permanent uses, by subtracting from them 
the whole effect of precession in the interval; and, more- 
over, to divest them of the influence of nutation by investi- 
gating and subducting the amount of change, both in right 
ascension and declination, due to the displacement of the 

6 This argument, cogent as it is, acquires additional and decisive force from 
the law of nutation, which is dependent on the position, for the time, of the 
lunar orbit. If we attribute it to a real motion of the celestial sphere, we must 
then maintain that sphere to be kept in a constant state of tremor by the motioa 
of the moon I 



OUTLINES OF ASTRONOMY 269 

pole from the centre to the circumference of the little ellipse 
above mentioned. This last process is technically termed 
correcting or equating the observation for nutation; by 
which latter word is always understood, in astronomy, the 
getting rid of a periodical cause of fluctuation, and present- 
ing a result, not as it was observed, but as it would have 
been observed, had that cause of fluctuation had no exist- 
ence. 

(325. ) For these purposes, in the present case, very con- 
venient formulae have been derived, and tables constructed. 
They are, however, of too technical a character for this 
work; we shall, however, 
point out the manner in 
which the investigation is 
conducted. It has been 
shown in art. 309 by what 
means the right ascension 
and declination of an object 
are derived from its longitude 
and latitude. Eeferring to 
the figure of that article, 
and supposing the triangle 
K P X orthographically projected on the plane of the eclip- 
tic as in the annexed figure: in the triangle K P X, K P is 
the obliquity of the ecliptic, K X the co-latitude (or comple- 
ment of latitude), and the angle P K X the co-longitude of 
the object X. These are the data of our question, of which 
the second is constant, and the other two are varied by the 
effect of precession and nutation: and their variations (con- 
sidering the minuteness of the latter effect generally, and the 
small number of years in comparison of the whole period of 
25,868, for which we ever require to estimate the effect of 




270 OUTLINES OF ASTRONOMY 

the former) are of that order which may be regarded as in- 
finitesimal in geometry, and treated as snch without fear of 
error. The whole question, then, is reduced to this: — In a 
spherical triangle K P X, in which one side K X is con- 
stant, and an angle K, and adjacent side K P vary by given 
infinitesimal changes of the position of P: required the 
changes thence arising in the other side P X, and the angle 
K P X. This is a very simple and easy problem of spher- 
ical geometry, and being resolved, it gives at once the re- 
ductions we are seeking; for P X being the polar distance 
of the object, and the angle K P X its right ascension plus 
90°, their variations are the very quantities we seek. It 
only remains, then, to express in proper form the amount of 
the precession and nutation in longitude and latitude, when 
their amount in right ascension and declination will immedi- 
ately be obtained. 

(326.) The precession in latitude is zero, since the lati- 
tudes of objects are not changed by it; that in longitude 
is a quantity proportional to the time at the rate of 50" -10 
per annum. With regard to the nutation in longitude and 
latitude, these are no other than the abscissa and ordinate 
of the little ellipse in which the pole moves. The law of 
its motion, however, therein, cannot be understood till the 
reader has been made acquainted with the principal features 
of the moon's motion on which it depends. 

(327.) Another consequence of what has been shown 
respecting precession and nutation, is that sidereal time, 
as astronomers use it, i.e. as reckoned from the transit of 
the equinoctial point, is not a mean or uniformly flowing 
quantity, being affected by nutation; and, moreover, that so 
reckoned, even when cleared of the periodical fluctuation 
of nutation, it does not strictly correspond to the earth's 



OUTLINES OF ASTRONOMY 271 

diurnal rotation. As the sun loses one day in the year on 
the stars, by its direct motion in longitude ; so the equinox 
gains one day in 25,868 years on them by its retrograda- 
tion. We ought, therefore, as carefully to distinguish be- 
tween mean and apparent sidereal as between mean and 
apparent solar time. 

(828.) Neither precession nor nutation change the ap- 
parent places of celestial objects inter se. We see them, 
so far as these causes go, as they are, though from a station 
more or less unstable, as we see distant land objects cor- 
rectly formed, though appearing to rise and fall when 
viewed from the heaving deck of a ship in the act of 
pitching and rolling. But there is an optical cause, inde- 
pendent of refraction or of perspective, which displaces 
them one among the other, and causes us to view the heav- 
ens under an aspect always to a certain slight extent false; 
and whose influence must be estimated and allowed for be- 
fore we can obtain a precise knowledge of the place of any 
object. This cause is what is called the aberration of light; 
a singular and surprising effect arising from this, that we 
occupy a station not at rest but in rapid motion ; and that 
the apparent directions of the rays of light are not the same 
to a spectator in motion as to one at rest. As the estima- 
tion of its effect belongs to uranography, we must explain 
it here, though, in so doing, we must anticipate some of 
the results to be detailed in subsequent chapters. 

(329.) Suppose a shower of rain to fall perpendicularly 
in a dead calm ; a person exposed to the shower, who should 
stand quite still and upright, would receive the drops on 
his hat, which would thus shelter him, but if he ran for- 
ward in any direction they would strike him in the face. 
The effect would be the same as if he remained still, and 



272 



OUTLINES OF ASTRONOMY 



a wind should arise of the same velocity, and drift them 
against him. Suppose a ball let fall from a point A above 
a horizontal line E F, and that at B were placed to receive 
it the open mouth of an inclined hollow tube P Q; if the 
tube were held immovable the ball would strike on its 
lower side, but if the tube were carried forward in the 
direction E F, with a velocity properly adjusted at every 
instant to that of the ball, while preserving its inclination 



Qa 




to the horizon, so that when the ball in its natural descent 
reached C, the tube should have been carried into the posi- 
tion E S, it is evident that the ball would, throughout its 
whole descent, be found in the axis- of the tube; and a 
spectator referring to the tube the motion of the ball, and 
carried along with the former, unconscious of its motion, 
would fancy that the ball had been moving in the inclined 
direction E S of the tube's axis. 

(330.) Our eyes and telescopes are such tubes. In what- 
ever manner we consider light, whether as an advancing 
wave in a motionless ether, or a shower of atoms traversing 
space (provided that in both cases we regard it as abso- 
lutely incapable of suffering resistance or corporeal obstruc- 
tion from the particles of transparent media traversed by 



OUTLINES OF ASTRONOMY 273 

it 7 ), if in the interval between the rays traversing the object- 
glass of the one or the cornea of the other (at which moment 
they acquire that convergence which directs them to a cer- 
tain point in fixed space), and their arrival at their focus, 
the cross wires of the one or the retina of the other be 
slipped aside, the point of convergence (which remains un- 
changed) will no longer correspond to the intersection of 
the wires or the central point of our visual area. The 
object then will appear displaced; and the amount of this 
displacement is aberration. 

(331.) The earth is moving through space with a velocity 
of about 19 miles per second, in an elliptic path round the 
sun, and is therefore changing the direction of its motion 
at every instant. Light travels with a velocity of 192,000 
miles per second, which, although much greater than that 
of the earth, is yet not infinitely so. Time is occupied by 
it in traversing any space, and in that time the earth de- 
scribes a space which is to the former as 19 to 192,000, 
or as the tangent of 20" *5 to radius. Suppose now APS 
to represent a ray of light from a star at A, and let the 
tube P Q be that of a telescope so inclined forward that 
the focus formed by its object-glass shall be received upon 
its cross wire, it is evident from what has been said that 
the inclination of the tube must be such as to make 
P S : S Q : : velocity of light : velocity of the earth : : 1 : 
tan. 20* -5; and, therefore, the angle S P Q, or P S E, by 

n This condition is indispensable. Without it we fall into all those diffi- 
culties which M. Doppler has so well pointed out in his paper on Aberration 
(Abhandlungen der k. boemischen GTesellschaft der Wissenschaften. Folge V. 
vol. iii.). If light itself, or the luminiferous ether, be corporeal, the condition 
insisted on amounts to a formal surrender of the dogma, either of the extension 
or of the impenetrability of matter; at least in the sense in which those terms 
have been hitherto used by metaphysicians. At the point to which science 
is arrived, probably few will be found disposed to maintain either the one or 
the other. 




274 OUTLINES OF ASTRONOMY 

which the axis of the telescope must deviate from the true 
direction of the star, must be 20" *5. 

(332.) A similar reasoning will hold good when the 
direction of the earth's motion is not perpendicular to 
the visual ray. If S B be the true direction of the visual 
ray, and A C the position in which the telescope requires 
to be held in the apparent direction, we must still have 
the proportion B C : B A : : veloc- 
ity of light : velocity of the earth 
: : rad. : sine of 20" 5 (for in such 
small angles it matters not whether 
we use the sines or tangents). But 
we have, also, by trigonometry, B C : B A : : sine of 
B A C: sine of A C B or C B P, which last is the appar- 
ent displacement caused by aberration. Thus it appears 
that the sine of the aberration, or (since the angle is ex- 
tremely small) the aberration itself, is proportional to the 
sine of the angle made by the earth's motion in space with 
the visual ray, and is therefore a maximum when the line 
of sight is perpendicular to the direction of the earth's 
motion. 

(333.) The uranographical effect of aberration, then, is 
to distort the aspect of the heavens, causing all the stars 
to crowd as it were directly toward that point in the 
heavens which is the vanishing point of all lines parallel 
to that in which the earth is for the moment moving. 
As the earth moves round the sun in the plane of the 
ecliptic, this point must lie in that plane, 90° in advance 
of the earth's longitude, or 90° behind the sun's, and shifts 
of course continually, describing the circumference of the 
ecliptic in a year. It is easy to demonstrate that the effect 
on each particular star will be to make it apparently de- 



OUTLINES OF ASTRONOMY 275 

scribe a small ellipse in the heavens, having for its centre 
the point in which the star would be seen if the earth 
were at rest. 

(334.) Aberration then affects the apparent right ascen- 
sions and declinations of all the stars, and that by quanti- 
ties easily calculable. The formulae most convenient for 
that purpose, and which, systematically embracing at the 
same time the corrections for precession and nutation, en- 
able the observer, with the utmost readiness, to disencum- 
ber his observations of right ascension and declination of 
their influence, have been constructed by Prof. Bessel, an^L 
tabulated in the appendix to the first volume of the Trans- 
actions of the Astronomical Society, where they will be 
found accompanied with an extensive catalogue of the 
places, for 1830, of the principal fixed stars, one of the 
most useful and best arranged works of the kind which 
has ever appeared. 

(335.) When the body from which the visual ray ema- 
nates is itself in motion, an effect arises which is not prop- 
erly speaking aberration, though it is usually treated under 
that head in astronomical books, and indeed confounded 
with it, to the production of some confusion in the mind 
of the student. The effect in question (which is indepen- 
dent of any theoretical views respecting the nature of light 8 ) 



8 The results of the undulatory and corpuscular theories of light, in the mat- 
ter of aberration, are, in the main, the same. We say in the main. There is, 
however, a minute difference even of numerical results. In the undulatory 
doctrine, the propagation of light takes place with equal velocity in all direc- 
tions, whether the luminary be at rest or in motion. In the corpuscular, with 
an excess of velocity in the direction of the motion over that in the contrary 
equal to twice the velocity of the body's motion. In the cases, then, of a body 
moving with equal velocity directly to and directly from the earth, the aberra- 
tions will be alike on the undulatory, but different on the corpuscular hypothe- 
sis. The utmost difference which can arise from this cause in owr system cannot 
amount to above six thousandths of a second. 



276 OUTLINES OF ASTRONOMY 

may be explained as follows. The ray by which we see 
any object is not that which it emits at the moment we 
look at it, but that which it did emit some time before, viz, 
the time occupied by light in traversing the interval which 
separates it from us. The aberration of such a body then 
arising from the earth's velocity must be applied as a cor- 
rection, not to the line joining the earth's place at the 
moment of observation with that occupied by the body 
at the same moment, but at that antecedent instant when 
the ray quitted it. Hence it is easy to derive the rule 
given by astronomical writers for the case of a moving 
object. From the known laws of its motion and the earth's, 
calculate its apparent or relative angular motion in the time 
taken by light to traverse its distance from the earth. This 
is the total amount of its apparent misplacement. Its effect 
is to displace the body observed in a direction contrary to 
its apparent motion in the heavens. And it is a compound 
or aggregate effect consisting of two parts, one of which is 
the aberration, properly so called, resulting from the com- 
position of the earth's motion with that of light, the other 
being what is not inaptly termed the Equation of light, being 
the allowance to be made for the time occupied by the light 
in traversing a variable space. 

(336.) The complete Reduction, as it is called, of an 
astronomical observation consists in applying to the place 
of the observed heavenly body as read off on the instru- 
ments (supposed perfect and in perfect adjustment) five dis- 
tinct and independent corrections, viz. those for refraction, 
parallax, aberration, precession, and nutation. Of these the 
correction for refraction enables us to declare what would 
have been the observed place, were there no atmosphere to 
displace it. That for parallax enables us to say from its 



OUTLINES OF ASTRONOMY 277 

place observed at the surface of the earth, where it would 
have been seen if observed from the centre. That for aber- 
ration, where it would have been observed from a motion- 
less, instead of a moving station: while the corrections for 
precession and nutation refer it to fixed and determinate 
instead of constantly varying celestial circles. The great 
importance of these corrections, which pervade all astron- 
omy, and have to be applied to every observation before it 
can be employed for any practical or theoretical purpose, 
•renders this recapitulation far from superfluous. 

(337.) Eefraction has been already sufficiently explained 
(art. 40), and it is only, therefore, necessary here to add that 
in its use as an astronomical correction its amount must 
be applied in a contrary sense to that in which it affects 
the observation; a remark equally applicable to all other 
corrections. 

(338.) The general nature of parallax or rather of par- 
allactic motion has also been explained in art. 80. But 
parallax in the uranographical sense of the word has a 
more technical meaning. It is understood to express that 
optical displacement of a body observed which is due to its 
being observed, not from that point which we have fixed 
upon as a conventional central station (from which we con- 
ceive the apparent motion would be more simple in its laws), 
but from some other station remote from such conventional 
centre: not from the centre of the earth, for instance, but 
from its surface: not from the centre of the sun (which, as 
we shall hereafter see, is for some purposes a preferable 
conventional station), but from that of the earth. In the 
former case this optical displacement is called the diurnal 
or geocentric parallax; in the latter the annual or helio- 
centric. In either case parallax is the correction to be ap- 



278 



OUTLINES OF ASTRONOMY 



plied to the apparent place of the heavenly body, as actually 
seen from the station of observation, to reduce it to its place 
as it would have been seen at that instant from the conven- 
tional station. 

(339.) The diurnal or geocentric parallax at any place of 
the earth's surface is easily calculated if we know the dis- 
tance of the body, and, vice 
versa, if we know the diurnal 
parallax that distance may be 
calculated. For supposing S 
the object, C the centre of 
the earth, A the station of ob- 
servation at its surface, and 
C A Z the direction of a per- 
pendicular to the surface at A, 
then will the object be seen 
from A in the direction A S, 
and its apparent zenith dis- 
tance will be Z A S; whereas, if seen from the centre, it 
will appear in the direction C S, with an angular distance 
from the zenith of A equal to Z C S ; so that Z A S — Z C S 
or A S C is the parallax. Now since by trigonometry C S i 
C A :: sin C A S = sin Z A S : sin A S C, it follows that 

Kadius of earth 




the sine of the parallax: 



.+ sin Z A S. 



Distance of body 
(340.) The diurnal or geocentric parallax, therefore, at a 
given place, and for a given distance of the body observed, 
is proportional to the sine of its apparent zenith distance, 
and is, therefore, the greatest when the body is observed 
in the act of rising or setting, in which case its parallax is 
called its horizontal parallax, so that at any other zenith 
distance, parallax = horizontal parallax -J- sine of apparent 



OUTLINES OF ASTRONOMY 279 

zenith distance, and since A C S is always less than Z A S 
it appears that the application of the reduction or correction 
for parallax always acts in diminution of the apparent zenith 
distance or increase of the apparent altitude or distance from 
the Nadir, i.e. in a contrary sense to that for refraction. 

(341. ) In precisely the same manner as the geocentric or 
diurnal parallax refers itself to the zenith of the observer 
for its direction and quantitative rule, so the heliocentric 
or annual parallax refers itself for its law to the point in 
the heavens diametrically opposite to the place of the sun 
as seen from the earth. Applied as a correction, its effect 
takes place in a plane passing through the sun, the earth, 
and the observed body. Its effect is always to decrease its 
observed distance from that point or to increase its angular 
distance from the sun. And its sine is given by the rela- 
tion, Distance of the observed body from the sun 2 distance 
of the earth from the sun : : sine of apparent angular dis- 
tance of the body from the sun (or its apparent elongation): 
sine of heliocentric parallax. 9 

(342.) On a summary view of the whole of the urano- 
graphical corrections, they divide themselves into two 
classes, those which do, and those which do not, alter the 
apparent configurations of the heavenly bodies inter se. 
The former are real, the latter technical corrections. The 
real corrections are refraction, aberration and parallax. 
The technical are precession and nutation, unless, indeed, 
we choose to consider parallax as a technical correction in- 
troduced with a view to simplification by a better choice 
of our point of sight. 



9 This account of the law of heliocentric parallax is in anticipation of what 
follows in a subsequent chapter, and will be better understood by the student 
when somewhat further advanced. 



280 OUTLINES OF ASTRONOMY 

(343.) The corrections of the first of these classes have 
one peculiarity in respect of their law, common to them all, 
which the student of practical astronomy will do well to fix 
in his memory. They all refer themselves to definite apexes or 
points of convergence in the sphere. Thus, refraction in its 
apparent effect causes all celestial objects to draw together 
or converge toward the zenith of the observer: geocentric 
parallax, toward his Nadir: heliocentric, toward the place 
of the sun in the heavens: aberration toward that point in 
the celestial sphere which is the vanishing point of all lines 
parallel to the direction of the earth's motion at the mo- 
ment, or (as will be hereafter explained) toward a point 
in the great circle called the ecliptic, 90° behind the sun's 
place in that circle. When applied as corrections to an 
observation, these directions are of course to be reversed. 

(344.) In the quantitative law, too, which this class of 
corrections follow, a like agreement takes place, at least 
as regards the geocentric and heliocentric parallax and 
aberration, in all three of which the amount of the correc- 
tion (or more strictly its sine) increases in the direct propor- 
tion of the sine of the apparent distance of the observed 
body from the apex appropriate to the particular correction 
in question. In the case of refraction the law is less simple, 
agreeing more nearly with the tangent than the sine of that 
distance, but agreeing with the others in placing the maxi- 
mum at 90° from its apex. 

(345.) As respects the order in which these corrections 
are to be applied to any observation, it is as follows: 
1. Eefraetion; 2. Aberration; 3. Geocentric Parallax; 4. 
Heliocentric Parallax; 5. Nutation; 6. Precession. Such, 
at least, is the order in theoretical strictness. But as the 
amount of aberration and nutation is in all cases a very 



OUTLINES OF ASTRONOMY 281 

minute quantity, it matters not in what order they are 
applied; so that for practical convenience they are always 
thrown together with the precession, and applied after the 
others. 



CHAPTER VI 

OF THE SUN'S MOTION AND PHYSICAL CONSTITUTION 

Apparent Motion of the Sun not Uniform — Its Apparent Diameter also 
Variable — Variation of its Distance Concluded — Its Apparent Orbit 
an Ellipse about the Focus — Law of the Angular Velocity — Equable 
Description of Areas — Parallax of the Sun — Its Distance and Magni- 
tude — Copernican Explanation of the Sun's Apparent Motion — Parallel- 
ism of the Earth's Axis — The Seasons — Heat Received from the Sun 
in Different Parts of the Orbit — Effect of Excentricity of the Orbit and 
Position of its Axis on Climate — Mean and True Longitudes of the Sun 
— Equation of the Centre — Sidereal, Tropical and Anomalistic Tears 
— Physical Constitution of the Sun — Its Spots — Faculse — Probable 
Nature and Cause of the Spots — Recent Discoveries of Mr, Dawes — 
Of Mr. Nasmyth — Rotation of the Sun on its Axis — Its Atmosphere 
— Supposed Clouds — Periodical Recurrence of a More and Less Spotted 
State of its Surface — Temperature of its Surface— Its Expenditure of 
Heat — Probable Cause of Solar Radiation 

(346.) In the foregoing chapters, it has been shown that 
the apparent path of the sun is a great circle of the sphere, 
which it performs in a period of one sidereal year. From 
this it follows, that the line joining the earth and sun lies 
constantly in one plane] and that, therefore, whatever be 
the real motion from which this apparent motion arises, 
it must be confined to one plane, which is called the plane 
of the ecliptic. 

(347.) We have already seen (art. 146) that the sun's 
motion in right ascension among the stars is not uniform. 
This is partly accounted for by the obliquity of the ecliptic, 
in consequence of which equal variations in longitude do 



282 OUTLINES OF ASTRONOMY 

not correspond to equal changes of right ascension. But 
if we observe the place of the sun daily throughout the 
year, by the transit and circle, and from these calculate 
the longitude for each day, it will still be found that, even 
in its own proper path, its apparent angular motion is far 
from uniform. The change of longitude in twenty-four 
mean solar hours averages 0° 59' 8"*33; but about the 31st 
of December it amounts to 1° V §"'9, and about the 1st of 
July is only 0° 57' 11* *5. Such are the extreme limits, and 
such the mean value of the sun's apparent angular velocity 
in its annual orbit. 

(348.) This variation of its angular velocity is accom- 
panied with a corresponding change of its distance from 
us. The change of distance is recognized by a variation 
observed to take place in its apparent diameter, when 
measured at different seasons of the year, with an instru- 
ment adapted for that purpose, called the heliometer,* or, by 
calculating from the time which its disk takes to traverse 
the meridian in the transit instrument. The greatest ap- 
parent diameter corresponds to the 1st of January, or to 
the greatest angular velocity, and measures 32' 36" -2, the 
least is 31' 32" *0; and corresponds tc the 1st of July; at 
which epochs, as we have seen, the angular motion is also 
at its extreme limit either way. Now, as we cannot suppose 
the sun to alter its real size periodically, the observed change 
of its apparent size can only arise from an actual change of 
distance. And the sines or tangents of such small arcs 
being proportional to the arcs themselves, its distances 
from us, at the above-named epoch, must be in the inverse 
proportion of the apparent diameters. It appears, therefore, 
that the greatest, the mean, and the least distances of the 

1 'HAios the sun, and jxcTpaw to measure. 



OUTLINES OF ASTRONOMY 283 

sun from us are in the respective proportions of the numbers 
1-01679, 1-00000, and 0-98321; and that its apparent angular 
velocity diminishes as the distance increases, and vice versd. 
(349.) It follows from this, that the real orbit of the sun, 
as referred to the earth supposed at rest, is not a circle with 
the earth in the centre. The situation of the earth within it 
is excentric, the excentricity amounting to 0*01679 of the 
mean distance, which may be regarded as our unit of meas- 
ure in this inquiry. But besides this, the form of the orbit 
is not circular, but elliptic. If from any point 0, taken to 
represent the earth, we draw a line, O A, in some fixed 
direction, from which we then set off a series of angles, 
A B, A O C, etc., equal to the observed longitudes of the 
sun throughout the year, and in these respective directions 
measure off from O the distances 
O A, O B, O C, etc., representing 
the distances deduced from the 
observed diameter, and then con- 
nect all the extremities A, B, C, 
etc., of these lines by a continu- 
ous curve, it is evident this will be a correct represen- 
tation of the relative orbit of the sun about the earth. 
Now, when this is done, a deviation from the circular 
figure in the resulting curve becomes apparent; it is found 
to be evidently longer than it is broad — that is to say, 
elliptic, and the point O to occupy, not the centre, but one 
of the foci of the ellipse. The graphical process here de- 
scribed is sufficient to point out the general figure of the 
curve in question; but for the purposes of exact verifica- 
tion, it is necessary to recur to the properties of the ellipse, 9 

2 See Conic Sections, by the Rev. H. P. Hamilton, or any other of the very 
numerous works on this subject. 




284 OUTLINES OF ASTRONOMY 

and to express the distance of any one of its points in terms 
of the angular situation of that point with respect to the 
longer axis, or diameter of the ellipse. This, however, is 
readily done ; and when numerically calculated, on the sup- 
position of the excentricity being such as above stated, a 
perfect coincidence is found to subsist between the distances 
thus computed, and those derived from the measurement of 
the apparent diameter. 

(350.) The mean distance of the earth and sun being 
taken for unity, the extremes are 1-01679 and 0*98321. But 
if we compare, in like manner, the mean or average angular 
velocity with the extremes, greatest and least, we shall find 
these to be in the proportions of 1*03386, 1*00000, and 
0*96670. The variation of the sun's angular velocity, then, 
is much greater in proportion than that of its distance — fully 
twice as great; and if we examine its numerical expressions 
at different periods, comparing them with the mean value, 
and also with the corresponding distances, it will be found, 
that, by whatever fraction of its mean value the distance ex- 
ceeds the mean, the angular velocity will fall short of its 
mean or average quantity by very nearly twice as great a 
fraction of the latter, and vice versa. Hence we are led to 
conclude that the angular velocity is in the inverse propor- 
tion, not of the distance simply, but of its square^ so that, 
to compare the daily motion in longitude of the sun, at one 
point, A, of its path, with that at B, we must state the pro- 
portion thus: — 

OB 3 : O A s : : daily motion at A : daily motion at B„ 
And this is found to be exactly verified in every part of the 
orbit. 

(351.) Hence we deduce another remarkable conclusion — 
viz. that if the sun be supposed really to move around the 



OUTLINES OF ASTRONOMY 285 

circumference of this ellipse, its actual speed cannot be uni- 
form, but must be greatest at its least distance and less at its 
greatest. For, were it uniform, the apparent angular veloc- 
ity would be, of course, inversely proportional to the dis- 
tance ; simply because the same linear change of place, being 
produced in the same time at different distances from the 
eye, must, by the laws of perspective, correspond to appa- 
rent angular displacements inversely as those distances. 
Since, then, observation indicates a more rapid law of 
variation in the angular velocities, it is evident that mere 
change of distance, unaccompanied with a change of actual 
speed, is insufficient to account for it; and that the increased 
proximity of the sun to the earth must be accompanied with 
an actual increase of its real velocity of motion along its 
path. 

(352.) This elliptic form of the sun's path, the excentric 
position of the earth within it, and the unequal speed with 
which it is actually traversed by the sun itself, all tend to 
render the calculation of its longitude from theory (i.e. from 
a knowledge of the causes and nature of its motion) difficult; 
and indeed impossible, so long as the law of its actual veloc- 
ity continues unknown. This law, however, is not imme- 
diately apparent. It does not come forward, as it were, and 
present itself at once, like the elliptic form of the orbit, by a 
direct comparison of angles and distances, but requires an 
attentive consideration of the whole series of observations 
registered during an entire period. It was not, therefore, 
without much painful and laborious calculation, that it was 
discovered by Kepler (who was also the first to ascertain the 
elliptic form of the orbit), and announced in the following 
terms: — Let a line be always supposed to connect the sun, 
supposed in motion, with the earth, supposed at rest; then 



286 OUTLINES OF ASTRONOMY 

as the sun moves along its ellipse, this line (which is called 
in astronomy the radius vector) will describe or sweep over 
that portion of the whole area or surface of the ellipse which 
is included between its consecutive positions: and the mo- 
tion of the sun will be such that equal areas are thus swept 
over by the revolving radius vector in equal times, in what- 
ever part of the circumference of the ellipse the sun may be 
moving. 

(353.) From this it necessarily follows, that in unequal 
times, the areas described must be proportional to the times. 
Thus, in the figure of art. 349 the time in which the sun 
moves from A to B, is to the time in which it moves from 
C to D, as the area of the elliptic sector A O B is to the area 
of the sector DOC. 

(354.) The circumstances of the sun's apparent annual 
motion may, therefore, be summed up as follows: — It is per- 
formed in an orbit lying in one plane passing through the 
earth's centre, called the plane of the ecliptic, and whose 
projection on the heavens is the great circle so called. In 
this plane its motion is from west to east, or to a spectator 
looking down on the plane of the elliptic from the northern 
side, in a direction the reverse of that of the hands of a 
watch laid face uppermost. In this plane, however, the 
actual path is not circular, but elliptical; having the earth, 
not in its centre, but in one focus. The excentricity of this 
ellipse is 0*01679, in parts of a unit equal to the mean dis- 
tance, or half the longer diameter of the ellipse; i.e. about one- 
sixtieth part of that semi- diameter; and the motion of the 
sun in its circumference is so regulated, that equal areas of 
the ellipse are passed over by the radius vector in equal 
times. 

(355.) What we have here stated supposes no knowledge 



OUTLINES OF ASTRONOMY 287 

of the sun's actual distance from the earth nor, conse- 
quently, of the actual dimensions of its orbit, nor of the 
body of the sun itself. To come to any conclusions on 
these points, we must first consider by what means we can 
arrive at any knowledge of the distance of an object to which 
we have no access. Now, it is obvious, that its parallax 
alone can afford us any information on this subject. Sup- 
pose P A B Q to represent the earth, C its centre, and S the 
sun, and A, B two situations of a spectator, or, which comes 
to the same thing, the stations of two spectators, both ob- 
serving the sun S at the same instant. The spectator A will 
see it in the direction A S a, and will refer it to a point a in 
the infinitely distant sphere of the fixed stars, while the 




spectator B will see it in the direction B S b, and refer it 
to b. The angle included between these directions, or the 
measure of the celestial arc a b } by which it is displaced, is 
equal to the angle A S B ; and if this angle be known, and 
the local situations of A and B, with the part of the earth's 
surface A B included between them, it is evident that the 
distance C S may be calculated. Now, since A S C (art. 
339) is the parallax of the sun as seen from A, and B S 
as seen from B, the angle A S B, or the total apparent dis- 
placement is the sum of the two parallaxes. Suppose, then, 
two observers — one in the northern, the other in the south- 
ern hemisphere — at stations on the same meridian, to ob- 
serve on the same day the meridian altitudes of the sun's 



288 OUTLINES OF ASTRONOMY 

centre. Having thence derived the apparent zenith dis- 
tances, and cleared them of the effects of refraction, if the 
distance of the sun were equal to that of the fixed stars, the 
sum of the zenith distances thus found would be precisely 
equal to the sum of the latitudes north and south of the 
places of observation. For the sum in question would then 
be equal to the angle Z C X, which is the meridional dis- 
tance of the stations across the equator. But the effect of 
parallax being in both cases to increase the apparent zenith 
distances, their observed sum will be greater than the sum 
of the latitudes, by the sum of the two parallaxes, or by the 
angle A S B. This angle, then, is obtained by subducting 
the sum of the north and south latitudes from that of the 
zenith distances; and this once determined, the horizontal 
parallax is easily found, by dividing the angle so determined 
by the sum of the sines of the two latitudes. 

(356.) If the two stations be not exactly on the same 
meridian (a condition very difficult to fulfil), the same proc- 
ess will apply, if we take care to allow for the change of the 
sun's actual zenith distance in the interval of time elapsing 
between its arrival on the meridians of the stations. This 
change is readily ascertained, either from tables of the sun's 
motion, grounded on the experience of a long course of ob- 
servations, or by actual observation of its meridional altitude 
on several days before and after that on which the observa- 
tions for parallax are taken. Of course, the nearer the sta- 
tions are to each other in longitude, the less is this interval 
of time, and, consequently, the smaller the amount of this 
correction; and, therefore, the less injurious to the accuracy 
of the final result is any uncertainty in the daily change of 
zenith distance which may arise from imperfection in the 
solar tables, or in the observations made to determine it. 



OUTLINES OF ASTRONOMY 289 

(357.) Tlie horizontal parallax of the sun has been con- 
cluded from observations of the nature above described, 
performed in stations the most remote from each other in 
latitude, at which observatories have been instituted. It 
has also been deduced from other methods of a more re- 
fined nature, and susceptible of much greater exactness, to 
be hereafter described. Its amount so obtained, is about 
8" # 6. Minute as this quantity is, there can be no doubt that 
it is a tolerably correct approximation to the truth; and in 
conformity with it, we must admit the sun to be situated at 
a mean distance from us, of no less than 23984 times the 
length of the earth's radius, or about 95000000 miles. [See 
Note F.] 

(358.) That at so vast a distance the sun should appear to 
us of the size it does, and should so powerfully influence our 
condition by its heat and light, requires us to form a very 
grand conception of its actual magnitude, and of the scale 
on which those important processes are carried on within it, 
by which it is enabled to keep up its liberal and 'unceasing 
supply of these elements. As to its actual magnitude we 
can be at no loss, knowing its distance, and the angles under 
which its diameter appears to us. An object, placed at the 
distance of 95000000 miles, and subtending an angle of 
32' V, must have a real diameter of 882000 miles. Such, 
then, is the diameter of this stupendous globe. If we com- 
pare it with what we have already ascertained of the dimen- 
sions of our own, we shall find that in linear magnitude it 
exceeds the earth in the proportion 111 \ to 1, and in bulk in 
that of 1384472 to 1. 

(359.) It is hardly possible to avoid associating* our con- 
ception of an object of definite globular figure, and of such 

enormous dimensions, with some corresponding attribute of 
Astronomy— Yol. XIX— 13 



290 OUTLINES OF ASTRONOMY 

massiveness and material solidity. That the sun is not a 
mere phantom, but a body having its own peculiar structure 
and economy, our telescopes distinctly inform us. They 
show us dark spots on its surface, which slowly change their 
places and forms, and by attending to whose situation, at 
different times, astronomers have ascertained that the sun 
revolves about an axis nearly perpendicular to the plane of 
the ecliptic, performing one rotation in a period of about 25 
days, and in the same direction with the diurnal rotation of 
the earth, i.e. from west to east. Here, then, we have an 
analogy with our own globe ; the slower and more majestic 
movement only corresponding with the greater dimensions 
of the machinery, and impressing us with the prevalence of 
similar mechanical laws, and of, at least, such a community 
of nature as the existence of inertia and obedience to force 
may argue. Now, in the exact proportion in which we in- 
vest our idea of this immense bulk with the attribute of 
inertia, or weight, it becomes difficult to conceive its circu- 
lation round so comparatively small a body as the earth, 
without, on the one hand, dragging it along, and displacing 
it, if bound to it by some invisible tie; or, on the other 
hand, if not so held to it, pursuing its course alone in space, 
and leaving the earth behind. If we connect two solid 
masses by a rod, and fling them aloft, we see them circulate 
about a point between them, which is their common centre 
of gravity; but if one of them be greatly more ponderous 
than the other, this common centre will be proportionally 
nearer to that one, and even within its surface; so that the 
smaller one will circulate, in fact, about the larger, which 
will be comparatively but little disturbed from its place. 

(360.) Whether the earth move round the sun, the sun 
round the earth, or both round their common centre of gray- 



OUTLINES OF ASTRONOMY 291 

ity, will make no difference, so far as appearances are con- 
cerned, provided the stars be supposed sufficiently distant 
to undergo no sensible apparent parallactic displacement by 
the motion so attributed to the earth. Whether they are so 
or not must still be a matter of inquiry ; and from the ab- 
sence of any measurable amount of such displacement, we 
can conclude nothing but this, that the scale of the sidereal 
universe is so great, that the mutual orbit of the earth and 
sun may be regarded as an imperceptible point in compari- 
son with the distance of its nearest members. Admitting, 
then, in conformity with the laws of dynamics, that two 
bodies connected with and revolving about each other in 
free space do, in fact, revolve about their common centre of 
gravity, which remains immovable by their mutual action, 
it becomes a matter of further inquiry, whereabouts between 
them this centre is situated. Mechanics teach us that its 
place will divide their mutual distance in the inverse ratio 
of their weights or masses; 5 and calculations grounded on 
phenomena, of which an account will be given further on, 
inform us that this ratio, in the case of the sun and earth, is 
actually that of 354936 to 1 — the sun being, in that propor- 
tion, more ponderous than the earth. From this it will fol- 
low that the common point about which they both circulate 
is only 267 miles from the sun's centre, or about simth part 
of its own diameter. 

(361.) Henceforward, then, in conformity with the above 
statements, and with the Copernican view of our system, we 
must learn to look upon the sun as the comparatively mo- 
tionless centre about which the earth performs an annual 
elliptic orbit of the dimensions and excentricity, and with a 

* Principia, lib. i. lex. iii. cor. 14. 



292 OUTLINES OF ASTRONOMY 

velocity, regulated according to the law above assigned ; the 
sun occupying one of the foci of the ellipse, and from that 
station quietly disseminating on all sides its light and heat; 
while the earth travelling round it, and presenting itself dif- 
ferently to it at different times of the year and day, passes 
through the varieties of day and night, summer and winter, 
which we enjoy; its motion (art. 354) being from west to 
east. 

(362.) In this annual motion of the earth, its axis pre- 
serves, at all times, the same direction as if the orbitual 
movement had no existence; and is carried round parallel 
to itself, and pointing always to the same vanishing point in 
the sphere of the fixed stars. This it is which gives rise to 
the variety of seasons, as we shall now explain. In so 
doing, we shall neglect (for a reason which will be pres- 
ently explained) the ellipticity of the orbit, and suppose it 
a circle, with the sun in the centre and the four quadrants 
of its orbit to be described in equal times, the motion in a 
circle being uniform. 




(363.) Let, then, S represent the sun, and A, B, C, B, 
four positions of the earth in its orbit 90° apart, viz. A 
that which, it has at the moment when the sun is opposite 
to the intersection of the plane of the ecliptic B Gr, with 
that of the equator F E; B that which it has a quarter 
of a year subsequently or 90° of longitude in advance of 



OUTLINES OF ASTRONOMY 293 

A; C, 180° and D, 270° in advance of A. In each of these 
positions let P Q represent the axis of the earth, about 
which its diurnal rotation is performed without interfering 
with its annual motion in its orbit. Then, since the sun 
can only enlighten one-half of the surface at once, viz. that 
turned toward it, the shaded portions of the globe in its 
several positions will represent the dark, and the bright, 
the enlightened halves of the earth's surface in these posi- 
tions. Now, 1st, in the position A, the sun is vertically 
over the intersection of the equinoctial F E and the ecliptic 
H Gr. It is, therefore, in the vernal equinox; and in this 
position the poles P, Q, both fall on the extreme confines 
of the enlightened side. In this position, therefore, it is 
day over half the northern and half the southern hemi- 
sphere at once; and as the earth revolves on its axis, 
every point of its surface describes half its diurnal course 
in light, and half in darkness; in other words, the duration 
of day and night is here equal over the whole globe: hence 
the term equinox. The same holds good at the autumnal 
equinox on the position C. 

(364.) B is the position of the earth at the time of the 
northern summer solstice. (See art. 389.) Here the north 
pole P, and a considerable portion of the earth's surface 
in its neighborhood, as far as B, are situated within the 
enlightened half. As the earth turns on its axis in this 
position, therefore, the whole of that part remains con- 
stantly enlightened; therefore, at this point of its orbit, or 
at this season of the year, it is continual day at the north 
pole, and in all that region of the earth which encircles this 
pole as far as B— that is, to the distance of 23° 27' 30' from 
the pole, or within what is called in geography the arctic 
circle. On the other hand, the opposite or south pole Q, 



294 OUTLINES OF ASTRONOMY 

with all the region comprised within the antarctic circle, as 
far as 23° 27' 30" from the south pole, are immersed at this 
season in darkness during the entire diurnal rotation, so 
that it is here continual night. 

(365.) With regard to that portion of the surface com- 
prehended between the arctic and antarctic circles, it is 
no less evident that the nearer any point is to the north 
pole, the larger will be the portion of its diurnal course 
comprised within the bright, and the smaller within the 
dark hemisphere; that is to say, the longer will be its day, 
and the shorter its night. Every station north of the equa- 
tor will have a day of more and a night of less than twelve 
hours' duration, and vice versa. All these phenomena are 
exactly inverted when the earth comes to the opposite 
point D of its orbit. 

(366.) Now, the temperature of any part of the earth's 
surface depends mainly on its exposure to the sun's rays. 
Whenever the sun is above the horizon of any place, that 
place is receiving heat; when below, parting with it, by the 
process called radiation; and the whole quantities received 
and parted with in the year (secondary causes apart) must 
balance each other at every station, or the equilibrium of 
temperature (that is to say, the constancy which is observed 
to prevail in the annual averages of temperature as indi- 
cated by the thermometer) would not be supported. When- 
ever, then, the sun remains more than twelve hours above 
the horizon of any place, and less beneath, the general tem- 
perature of that place will be above the average; when the 
reverse, below. As the earth, then, moves from A to B, 
the days growing longer, and the nights shorter in the 
northern hemisphere, the temperature of every part of that 
hemisphere increases, and we pass from spring to summer; 



OUTLINES OF ASTRONOMY 295 

while, at the same time, the reverse obtains in the southern 
hemisphere. As the earth passes from B to C, the days 
and nights again approach to equality — the excess of tem- 
perature in the northern hemisphere above the mean state 
grows less, as well as its defect in the southern; and at the 
autumnal equinox C, the mean state is once more attained. 
From thence to D, and, finally, round again to A, all the 
same phenomena, it is obvious, must again occur, but re- 
versed — it being now winter in the northern and summer 
in the southern hemisphere. 

(367.) All this is consonant to observed fact. The con- 
tinual day within the polar circles in summer, and night 
in winter, the general increase of temperature and length of 
day as the sun approaches the elevated pole, and the re- 
versal of the seasons in the northern and southern hemi- 
spheres, are all facts too well known to require further 
comment. The positions A, C of the earth correspond, as 
we have said, to the equinoxes; those at B, ~D to the sol- 
stices. This term must be explained. If, at any point, X, 
of the orbit, we draw X P the earth's axis, and X S to 
the sun, it is evident that the angle P X S will be the 
sun's polar distance. Now this angle is at its maximum 
in the position D, and at its minimum at B: being in the 
former case = 90° + 23° 28' = 113° 28', and in the latter 
90° _ 23° 28' = 66° 32'. At these points the sun ceases 
to approach to or to recede from the pole, and hence the 
name solstice. 

(368 a.) Let us next consider how these phenomena are 
modified by the ellipticity of the earth's orbit and the po- 
sition of its longer axis with respect to the line of the sol- 
stices. This ellipticity (art. 350) is about one-sixtieth of 
the mean distance, so that the sun, at its greatest proximity 



296 OUTLINES OF ASTRONOMY 

is about one-thirtieth of its mean distance nearer us than 
when most remote. Since light and heat are equally dis- 
persed from the sun in all directions, and are spread, in 
diverging, over the surface of a sphere enlarging as they 
recede from the centre, they must diminish in intensity 
according to the inverse proportion of the surfaces over 
which they are spread, i.e. in the inverse ratio of the 
squares of the distances. Hence the hemisphere opposed 
to the sun will receive in a given time, when nearest, two- 
thirtieths or one-fifteenth more heat and light than when 
most remote, as may be shown by an easy calculation. 4 
Now, the sun's longitude when at its least distance from 
the earth (at which time it is said to be in perigee and the 
earth in its perihelion 6 ) is at present 280° 28' in which posi- 
tion it is on the 1st of January, or eleven days after the 
time of the winter solstice of the northern hemisphere; or, 
which is the same thing, the summer solstice of the southern 
(art. 364), while on the other hand the sun is most remote 
(in apogee or the earth in its aphelion 9 ), when in longitude 
100° 28' or on the 2d of July, i.e. eleven days after the 
epoch of the northern summer or southern winter solstice. 
We shall suppose, however, for simplicity of explanation, 
the perigee and apogee to be coincident with the solstice. 
At and about the southern summer solstice then, the whole 
earth is receiving per diem the greatest amount of heat that 
it can receive, and of this the southern hemisphere receives 
the larger share, because its pole and the whole region 
within the antarctic circle is in perpetual sunshine, while 



4 (g)*= © 3 very nearly, - (*)■_ » = 8 very nearly, - g. 

8 wept, about or in the neighborhood of ; n* the earth ; n**os, the sun. 

6 aw6 t away from. 



OUTLINES OF ASTRONOMY 297 

the corresponding northern regions lie in shadow. On the 
other hand, at and about the northern summer solstice, 
although it is true that the reverse conditions as to the 
regions illuminated prevail, jet the whole earth is then re- 
ceiving per diem less heat owing to the sun's remoteness: 
so that on the whole if the seasons were of equal duration, 
or in other words, if the angular movement of the earth 
in its elliptic orbit were uniform, the southern hemisphere 
would receive more heat per annum than the northern, and 
would consequently have a warmer mean temperature. 

(368 b.) Such, however, is not the case. The angular 
velocity of the earth in its orbit, as we have seen (art. 350), 
is not uniform, but varies in the inverse ratio of the square 
of the sun's distance, that is, in the same precise ratio as 
his heating power. The momentary supply of heat then 
received by the earth in every point of its orbit varies 
exactly as the momentary increase of its longitude, from 
which it obviously follows, that equal amounts of heat are 
received from the sun in passing over equal angles round 
it, in whatever part of the ellipse those angles may be sit- 
uated. Supposing the orbit, then, to be divided into two 
segments by any straight line drawn through the sun, since 
equal angles in longitude (180°) are described on either side 
of this line, the amount of heat received will be equal. In 
passing then from either equinox to the other, the whole 
earth receives equal amount of heat, the inequality in the 
intensities of solar radiation in the two intervals being pre- 
cisely compensated by the opposite inequality in the dura- 
tion of the intervals themselves; which amounts to about 
7i days, by which the northern spring and summer are to- 
gether longer than the southern. For these intervals are 
to each other in the proportion of the two unequal seg- 



298 OUTLINES OF ASTRONOMY 

ments of the whole ellipse into which the line of the 
equinoxes divides it. (See art. 353.) 

(368 c.) In what regards the comfort of a climate and 
the character of its vegetation, the intensity of a summer 
is more naturally estimated by the temperature of its hot- 
test day, and that of a winter by its sharpest frosts, than 
by the mere durations of those seasons and their total 
amount of heat. Supposing the excentricity of the earth's 
orbit were very much greater than it actually is; the posi- 
tion of its perihelion remaining the same; it is evident that 
the characters of the seasons in the two hemispheres would 
be strongly contrasted. In the northern, we should have 
a short but very mild winter with a long but very cool 
summer — i.e. an approach to perpetual spring; while the 
southern hemisphere would be inconvenienced and might 
be rendered uninhabitable by the fierce extremes caused by 
concentrating half the annual supply of heat into a summer 
of very short duration and spreading the other half over 
a long and dreary winter, sharpened to an intolerable in- 
tensity of frost when at its climax by the much greater 
remoteness of the sun. 

(369.) As it is, the difference, except under peculiar 
circumstances, is not very striking, being masked to a cer- 
tain extent by the action of another very influential cause 
to be explained in art. 370. This does not prevent, how- 
ever, the direct impression of the solar heat in the height of 
summer — the glow and ardor of his rays, under a perfectly 
clear sky, at noon, in equal latitudes and under equal 
circumstances of exposure — from being materially greater 
in the southern hemisphere than in the northern. One- 
fifteenth is too considerable a fraction of the whole in- 
tensity of sunshine not to aggravate in a serious degree 



OUTLINES OF ASTRONOMY 299 

the sufferings of those for instance who are exposed to it 
in thirsty deserts, without shelter. The accounts of these 
sufferings in the interior of Australia are of the most 
frightful kind, and would seem far to exceed what have 
ever been undergone by travellers in the northern deserts 
of Africa. 7 

(369 a.) It must be observed, moreover, that in estimat- 
ing the effect of any additional fraction (as one-fifteenth) of 
solar radiation on temperature, we have to consider as our 
unit, not the number of degrees above a purely arbitrary 
zero point (such as the freezing-point of water or the zero 
of Fahrenheit's scale) at which a thermometer stands in a 
hot summer day, as compared with a cold winter one, but 
the thermometric interval between the temperatures it indi- 
cates in the two cases, and that which it would indicate did 
the sun not exist, which there is good reason to believe 9 
would be at least as low as 239° below zero of Fahrenheit. 
And as a temperature of 100° Fahrenheit above zero is no 
uncommon one in a fair shade exposure under a sun nearly 
vertical, we have to take one-fifteenth of the sum of these 
intervals (339°), or 23° Fahrenheit, as the least variation of 
temperature under such circumstances which can reasonably 
be attributed to the actual variation of the sun's distance. 

(369 b.) In what has been premised we have supposed the 
situation of the axis of the earth's orbit to coincide with 
the line of the solstices, neglecting the difference of about 



7 See the account of Captain Sturt's exploration in Athenaeum, No. 1012. 
"The ground was almost a molten surface, and if a match accidentally fell upon 
it, it immediately ignited." The author has observed the temperature of the sur- 
face soil in South Africa as high as 159* Fahrenheit. An ordinary lucifer match 
does not ignite when simply pressed upon a smooth surface at 212°, but in the 
act of withdrawing it, it takes fire, and the slightest friction upon such a surface 
of course ignites it. 

8 See Meteorology, Encycl. Brit, (new edition) Art. 36. 



300 OUTLINES OF ASTRONOMY 

eleven days' motion at present existing between them. But 
this near coincidence has not always been the state of 
things, and will not always continue to be so. By the 
effect of precession (art. 312), both the line of equinoxes 
and those of solstices retreat on the ecliptic by an annual 
angular movement of 50"*1, which cause alone would carry 
them round, with respect to the axis of the earth's ellipse 
through a complete revolution, in 25868 years. And in this 
period, supposing the axis to retain a fixed position, the 
perihelion would come to coincide successively in longitude 
with both the solstices and with both the equinoxes. But, 
besides this, owing to the operation of causes hereafter to 
be explained, the axis does not remain so fixed, but shifts 
its position, with a much slower angular movement, of ll ff, 8 
per annum in the opposite direction to that in which preces- 
sion carries the line of equinoxes, and by which movement 
alone, if uniformly continued, the direction of the axis itself 
would be carried entirely round the whole circumference of 
the ecliptic in an immensely long period (no less than 109830 
years). Thus then we see that the vernal equinox and the 
perihelion recede from each other by the joint annual 
amount of 61* -9 or a degree in 58*16 years, which is, in 
effect, the same as if the perihelion made a complete revo- 
lution with reference to a fixed equinox in 20984 years. In 
consequence of this joint variation then, the place of the 
perihelion must have coincided with the vernal equinox 
(or have been situated in longitude 0°) about 4000 years 
before the Christian era, and in longitude 90° about A.D. 
1250, and will be situated in longitudes 180° and 270° 
respectively about the years A.D. 6500 and 11700. At 
the latter of these epochs, the case we have considered in 
the foregoing articles (368 a. et seq.) will be reversed, and the 



OUTLINES OF ASTRONOMY 301 

extreme summer and winter of the southern hemisphere will 
be transferred to the northern. 

(369 c.) In the immense periods which geologists con- 
template in the past history of the earth, this alternation 
of climates must have happened, not once only, but thou- 
sands of times, and it is not impossible that some of the 
indications which they have discovered of the prevalence at 
some former epoch or epochs of widely different climates from 
the present in the northern hemisphere, may be referable, 
in part at least, to this cause, though we are very far from 
supposing it competent (even taken in conjunction with 
other variations to be explained further on, which will 
sometimes go to exaggerate and sometimes to palliate its 
influence) to account for the whole of the changes which 
appear to have taken place. 9 

(370.) A conclusion of a very remarkable kind, recently 
drawn by Professor Dove from the comparison of ther- 
mometric observations at different seasons in very remote 
regions of the globe, may appear on first sight at variance 
with much that is above stated. That eminent meteorolo- 
gist has shown, by taking at all seasons the mean of the 
temperatures of points diametrically opposite to each other, 
that the mean temperature of the whole earth's surface in 
June considerably exceeds that in December. This result, 



9 M. Reynaud (Extrait de Philosophic religieuse. Paria: Imprimerie Du- 
vergne) attributes more influence to this cause, in historical times, than we 
should be disposed to allow it, when, for instance, he would explain by it the 
almost total disappearance of the date palm from Judaea since the time of Piiny, 
at which it appears to have flourished in perfection. At that epoch, however, 
the perihelion occupied a situation only 20° from the December solstice ; which 
implies a difference between the sun's perihelial and solstitial distances not ex- 
ceeding a thousandth part of its mean distance, corresponding to a difference of 
a five-hundredth part in the solar radiation. The effect of this, reckoned on the 
principles explained in the text, would not exceed two-thirds of a degree Fahr. 
in the midsummer temperature of Judaea at noon. See also his "Discours sur 
la Constitution physique de la Terre" (Encyclopedie Nouvelle). 



S02 OUTLINES OF ASTRONOMY 

which is at variance with the greater proximity of the sua 
in December, is, however, due to a totally different and 
very powerful cause — the greater amount of land in that 
hemisphere which has its summer solstice in June (i.e. the 
northern, see art. 362); and the fact is so explained by him. 
The effect of land under sunshine is to throw heat into the 
general atmosphere, and so distribute it by the carrying 
power of the latter over the whole earth. Water is much 
less effective in this respect, the heat penetrating its depths, 
and being there absorbed; so that the surface never acquires 
a very elevated temperature even under the equator. 

(371.) The great key to simplicity of conception in as- 
tronomy, and, indeed, in all sciences where motion is con- 
cerned, consists in contemplating every movement as re- 
ferred to points which are either permanently fixed, or so 
nearly so as that their motions shall be too small to inter- 
fere materially with and confuse our notions. In the choice 
of these primary points of reference, too, we must endeavor, 
as far as possible, to select such as have simple and sym- 
metrical geometrical relations of situation with respect to 
the curves described by the moving parts of the system, 
and which are thereby fitted to perform the office of natural 
centres — advantageous stations for the eye of reason and 
theory. Having learned to attribute an orbital motion to 
the earth, it loses this advantage, which is transferred to the 
sun, as the fixed centre about which its orbit is performed. 
Precisely as, when embarrassed by the earth's diurnal mo- 
tion, we have learned to transfer, in imagination, our station 
of observation from its surface to its centre, by the applica- 
tion of the diurnal parallax; so, when we come to inquire 
into the movements of the planets, we shall find ourselves 
continually embarrassed by the orbital motion of our point 



OUTLINES OF ASTRONOMY 803 

of view, unless, by the consideration of the annual or helio- 
centric parallax, we consent to refer all our observations on 
them to the centre of the sun, or rather to the common 
centre of gravity of the sun, and the other bodies which 
are connected with it in our system. 

(372.) Hence arises the distinction between the geocentric 
and heliocentric place of an object. The former refers its 
situation in space to an imaginary sphere of infinite radius, 
having the centre of the earth for its centre — the latter to 
one concentric with the sun. Thus, when we speak of the 
heliocentric longitudes and latitudes of objects, we suppose 
the spectator situated in the sun, and referring them by 
circles perpendicular to the plane of the ecliptic, to the 
great circle marked out in the heavens by the infinite pro- 
longation of that plane. 

(373.) The point in the imaginary concave of an infinite 
heaven, to which a spectator in the sun refers the earth, 
must, of course, be diametrically opposite to that to which 
a spectator on the earth refers the sun's centre; consequently 
the heliocentric latitude of the earth is always nothing, and 
its heliocentric longitude always equal to the sun's geocentric 
longitude +180°. The heliocentric equinoxes and solstices 
are, therefore, the same as the geocentric reversely named; 
and to conceive them, we have only to imagine a plane 
passing through the sun's centre, parallel to the earth's 
equator, and prolonged infinitely on all sides. The line of 
intersection of this plane and the plane of the ecliptic is the 
line of equinoxes, and the solstices are 90° distant from it. 

(374.) Were the earth's orbit a circle, described with a 
uniform velocity about the sun placed in its centre, nothing 
could be easier than to calculate its position at any time 
with respect to the line of equinoxes, or its longitude, for 



§04 OUTLINES OF ASTRONOMY 

vre should only have to reduce to numbers the proportion 
following; viz. One year : the time elapsed : : 360°: the arc 
of longitude passed over. The longitude so calculated is 
called in astronomy the mean longitude of the earth. But 
since the earth's orbit is neither circular, nor uniformly 
described, this rule will not give us the true place in the 
orbit at any proposed moment. Nevertheless, as the excen- 
tricity and deviation from a circle are small, the true place 
will never deviate very far from that so determined (which, 
for distinction's sake, is called the mean place), and the 
former may at all times be calculated from the latter, by 
applying to it a correction or equation (as it is termed), 
whose amount is never very great, and whose computation 
is a question of pure geometry, depending on the equable 
description of areas by the earth about the sun. For since, 
in elliptic motion according to Kepler's law above stated, 
areas not angles are described uniformly, the proportion 
must now be stated thus; — One year : the time elapsed : : 
the whole area of the ellipse : the area of the sector swept 
over by the radius vector in that time. This area, there- 
fore, becomes known, and it is then, as above observed, a 
problem of pure geometry to ascertain the angle about the 
sun (X S Z, fig. art. 362), which corresponds to any pro- 
posed fractional area of the whole ellipse supposed to be 
contained in the sector X Z S. Suppose we set out from 
X, the perihelion, then will the angle X S Z at first increase 
more rapidly than the mean longitude, and will, therefore, 
during the whole semi-revolution from A to M, exceed it 
in amount; or, in other words, the true place will be in 
advance of the mean: at M, one half the year will have 
eiapsed, and one half the orbit have been described, whether 
it be circular or elliptic. Here, then, the mean and true 



OUTLINES OF ASTRONOMY 305 

places coincide; but in all the other half of the orbit, from 
M to A, the true place will fall short of the mean, since at 
M the angular motion is slowest, and the true place from 
this point begins to lag behind the mean — to make up with 
it, however, as it approaches A, where it once more over- 
takes it. 

(375.) The quantity by which the true longitude of the 
earth differs from the mean longitude is called the equation 
of the centre, and is additive during all the half-year in 
which the earth passes from A to M, beginning at 0° 0' 0", 
increasing to a maximum, and again diminishing to zero at 
M ; after which it becomes sub tractive, attains a maximum 
of subtractive magnitude between M and A, arid again 
diminishes to at A. Its maximum, both additive and 
subtractive, is 1° 55' 33" -3. 

(376.) By applying, then, to the earth's mean longitude 
the equation of the centre corresponding to any given time 
at which we would ascertain its place, the true longitude 
becomes known ; and since the sun is always seen from the 
earth in 180° more longitude than the earth from the sun, 
in this way also the sun's true place in the ecliptic becomes 
known. The calculation of the equation of the centre is 
performed by a table constructed for that purpose, to be 
found in all "Solar Tables." 

(377.) The maximum value of the equation of the centre 
depends only on the ellipticity of the orbit, and may be ex- 
pressed in terms of the excentricity. Vice versd, therefore, 
if the former quantity can be ascertained by observation, the 
latter may be derived from it; because, whenever the law, 
or numerical connection, between two quantities is known, 
the one can always be determined from the other. Now, by 
assiduous observation of the sun's transits over the merid- 



806 OUTLINES OF ASTRONOMY 

ian, we can ascertain , for every day, its exact right ascen- 
sion, and thence conclude its longitude (art. 309). After 
this, it is easy to assign the angle by which this observed 
longitude exceeds or falls short of the mean ; and the great- 
est amount of this excess or defect which occurs in the 
whole year is the maximum equation of the centre. This, 
as a means of ascertaining the excentricity of the orbit, is a 
far more easy and accurate method than that of concluding 
the sun's distance by measuring its apparent diameter. The 
results of the two methods coincide, however, perfectly. 

(378.) If the ecliptic coincided with the equinoctial, the 
effect of the equation of the centre, by disturbing the uni- 
formity of the sun's apparent motion in longitude, would 
cause an inequality in its time of coming on the meridian 
on successive days. When the sun's centre comes to the 
meridian, it is apparent noon, and if its motion in longitude 
were uniform, and the ecliptic coincident with the equinoc- 
tial, this would always coincide with the mean noon, or the 
stroke of 12 on a well-regulated solar clock. But, inde- 
pendent of the want of uniformity in its motion, the ob- 
liquity of the ecliptic gives rise to another inequality in this 
respect; in consequence of which, the sun, even supposing 
its motion in the ecliptic uniform, would yet alternately, in 
its time of attaining the meridian, anticipate and fall short 
of the mean noon as shown by the clock. For the right as- 
cension of a celestial object forming a side of a right-angled 
spherical triangle, of which its longitude is the hypothenuse, 
it is clear that the uniform increase of the latter must neces- 
sitate a deviation from uniformity in the increase of the 
former. 

(379.) These two causes, then, acting conjointly, pro- 
duce, in fact, a very considerable fluctuation in the time as 



OUTLINES OF ASTRONOMY 307 

shown per clock, when the sun really attains the meridian. 
It amounts, in fact, to upward of half an hour; apparent 
noon sometimes taking place as much as 16i min. before 
mean noon, and at others as much as 14£ min. after. This 
difference between apparent and mean noon is called the 
equation of time, and is calculated and inserted in ephemer- 
ides for every day of the year, under that title: or else, 
which comes to the same thing, the moment, in mean time, 
of the sun's culmination for each day, is set down as an 
astronomical phenomenon to be observed. 

(380.) As the sun, in its apparent ann ual course, is car- 
ried along the ecliptic, its declination is continually varying 
between the extreme limits of 23° 27' 30" north, and as much 
south, which it attains at the solstices. It is consequently 
always vertical over some part or other of that zone or belt 
of the earth's surface which lies between the north and 
south parallels of 23° 27' 30". These parallels are called in 
geography the tropics-, the northern one that of Cancer, and 
the southern, of Capricorn-, because the sun, at the respec- 
tive solstices, is situated in the divisions, or signs of the 
ecliptic so denominated. Of these signs there are twelve, 
each occupying 30° of its circumference. They commence 
at the vernal equinox, and are named in order — Aries, 
Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagit- 
tarius, Capricornus, Aquarius, Pisces. 10 They are denoted 
also by the following symbols: — °P, \S, n, 2S, &, ^, =&, n\,, /, 
Y5> C#, X- Longitude itself is also divided into signs, de- 
grees, and minutes, etc. Thus 5 s 27° 0' corresponds to 
177° 0'. 

10 They may be remembered by the following memorial hexameters: — 
Sunt Aries, Taurus, Gemini, Cancer, Leo, Virgo, 
Libraque, Scorpius, Arcitenens, Caper, Amphora, Pisces. 



SOS OUTLINES OF ASTRONOMY 

(381.) These Signs are purely technical subdivisions of 
the ecliptic, commencing from the actual equinox, and are 
not to be confounded with the constellations so called (and 
sometimes so symbolized). The constellations of the zodiac, 
as they now stand arranged on the ecliptic, are all a full 
"sign" in advance or anticipation of their symbolic cogno- 
mens thereon marked. Thus the constellation Aries actu- 
ally occupies the sign Taurus 8 , the constellation Taurus, 
the sign Gemini n, and so on, the signs having retreated " 
among the stars (together with the equinox their origin), by 
the effect of precession. The bright star Spica in the con- 
stellation Yirgo (a Yirginis), by the observations of Hippar- 
chus, 128 years B.C., preceded, or was westward of the 
autumnal equinox in longitude by 6°. In 1750 it followed 
or stood eastward of the same equinox by 20° 21'. Its place 
then, as referred to the ecliptic at the former epoch, would 
be in longitude 5 s 24° 0', or in the 24th degree of the sign $,, 
whereas in the latter epoch it stood in the 21st degree of itg, 
the equinox having retreated by 26° 21' in the interval, 1878 
years, elapsed. To avoid this source of misunderstanding, 
the use of " signs" and their symbols in the reckoning of 
celestial longitudes is now almost entirely abandoned, and 
the ordinary reckoning (by degrees, etc., from to 360) 
adopted in its place, and the names Aries, Yirgo, etc., are 
becoming restricted to the constellations so called." 

(382.) When the sun is in either tropic, it enlightens, as 
we have seen, the pole on that side the equator, and shines 

11 Retreated is here used with reference to longitude, not to the apparent 
diurnal motion. 

12 When, however, the place of the sun is spoken of, the old usage prevails. 
Thus, if we say "the sun is in Aries," it would be interpreted to mean between 
0° and 30° of longitude. So, also, "the first point of Aries" is still understood 
to mean the vernal, and "the first point of Libra," the autumnal equinox; and 
so in a few other cases. 



OUTLINES OF ASTRONOMY 309 

over or beyond it to the extent of 23° 27' 30". The parallels 
of latitude, at this distance from either pole, are called the 
polar circles, and are distinguished from each other by the 
names arctic and antarctic. The regions within these circles 
are sometimes termed frigid zones, while the belt between 
the tropics is called the torrid zone, and the intermediate 
belts temperate zones. These last, however, are merely 
names given for the sake of naming; as, in fact, owing to 
the different distribution of land and sea in the two hemi- 
spheres, zones of climate are not co- terminal with zones of 
latitude. 

(383.) Our seasons are determined by the apparent pas- 
sages of the sun across the equinoctial, and its alternate 
arrival in the northern and southern hemisphere. Were 
the equinox invariable, this would happen at intervals pre- 
cisely equal to the duration of the sidereal year; but, in 
fact, owing to the slow conical motion of the earth's axis 
described in art. 317, the equinox retreats on the ecliptic, 
and meets the advancing sun somewhat before the whole 
sidereal circuit is completed. The annual retreat of the 
equinox is 50"*1, and this arc is described by the sun in 
the ecliptic in 20 m 19 s *9. By so much shorter, then, is the 
periodical return of our seasons than the true sidereal revo- 
lution of the earth round the sun. As the latter period, or 
sidereal year, is equal to 365 d 6 h 9 m 9 S *6, it follows, then, that 
the former must be only 365 d 5 h 48 m 49 9 *7; and this is what 
is meant by the tropical year. 

(384.) We have already mentioned that the longer axis 
of the ellipse described by the earth has a slow motion of 
11" 8 per annum in advance. From this it results, that 
when the earth, setting out from the perihelion, has com- 
pleted one sidereal period, the perihelion will have moved 



310 OUTLINES OF ASTRONOMY 

forward by 11* -8, which, arc must be described by the earth 
before it can again reach the perihelion. In so doing, it 
occupies 4 m 39 8 *7, and this must therefore be added to the 
sidereal period, to give the interval between two consecu- 
tive returns to the perihelion. This interval, then, is 
365 d 6 h 13 m 49 8 *3, 13 and is what is called the anomalistic 
year. All these periods have their uses in astronomy; but 
that in which mankind in general are most interested is the 
tropical year, on which the return of the seasons depends, 
and which we thus perceive to be a compound phenomenon, 
depending chiefly and directly on the annual revolution of 
the earth round the sun, but subordinately also, and indi- 
rectly, on its rotation round its own axis, which is what oc- 
casions the precession of the equinoxes; thus affording an 
instructive example of the way in which a motion, once ad- 
mitted in any part of our system, may be traced in its influ- 
ence on others with which at first sight it could not possibly 
be supposed to have anything to do. 

(385.) As a rough consideration of the appearance of the 
earth points out the general roundness of its form, and more 
exact inquiry has led us first to the discovery of its elliptic 
figure, and, in the further progress of refinement, to the per- 
ception of minuter local deviations from that figure; so, in 
investigating the solar motions, the first notion we obtain is 
that of an orbit, generally speaking, round, and not far from 
a circle, which, on more careful and exact examination, 
proves to be an ellipse of small excentricity, and described 
in conformity with certain laws, as above stated. Still 
minuter inquiry, however, detects yet smaller deviations 



13 These numbers, as well as most of the other numerical data of our system, 
are taken from Mr. Baily's Astronomical Tables and Formulae. 



OUTLINES OF ASTRONOMY 311 

again from this form and from these laws, of which, we have 
a specimen in the slow motion of the axis of the orbit 
spoken of in art. 372; and which are generally compre- 
hended under the name of perturbations and secular in- 
equalities. Of these deviations, and their causes, we shall 
speak hereafter at length. It is the triumph of physical 
astronomy to have rendered a complete account of them all, 
and to have left nothing unexplained, either in the motions 
of the sun or in those of any other of the bodies of our sys- 
tem. But the nature of this explanation cannot be under- 
stood till we have developed the law of gravitation, and car- 
ried it into its more direct consequences. This will be the 
object of our three following chapters; in which we shall 
take advantage of the proximity of the moon, and its imme- 
diate connection with and dependence on the earth, to ren- 
der it, as it were, a stepping-stone to the general explanation 
of the planetary movements. We shall conclude this by 
describing what is known of the physical constitution of 
the sun. 

(386.) When viewed through powerful telescopes, pro- 
vided with colored glasses, to take off the heat, which would 
otherwise injure our eyes, the sun is observed to have fre- 
quently large and perfectly black spots upon it, surrounded 
with a kind of border, less completely dark, called a penum- 
bra. Some of these are represented at a, 6, c, d, in Plate I. 
fig. 2, at the end of this volume. They are, however, not 
permanent. When watched from day to day, or even from 
hour to hour, they appear to enlarge or contract, to change 
their forms, and at length to disappear altogether, or to 
break out anew in parts of the surface where none were be- 
fore. In such cases of disappearance, the central dark spot 
always contracts into a point, and vanishes before the bor- 



512 OUTLINES OF ASTRONOMY 

der. Occasionally they break up, or divide into two or 
more, and in those cases offer every evidence of that ex- 
treme mobility which belongs only to the fluid state, and of 
that excessively violent agitation which seems only compati- 
ble with the atmospheric or gaseous state of matter. The 
scale on which their movements take place is immense. A 
single second of angular measure, as seen from the earth, 
corresponds on the sun's disk to 461 miles; and a circle of 
this diameter (containing therefore nearly 167000 square 
miles) is the least space which can be distinctly discerned 
on the sun as a visible area. Spots have been observed, 
however, whose linear diameter has been upward of 45000 
miles; 14 and even, if some records are to be trusted, of very 
much greater extent. 16 That such a spot should close up in 
six weeks' time (for they seldom last much longer), its bor- 
ders must approach at the rate of more than 1000 miles a 
day. 

(387.) Many other circumstances tend to corroborate this 
view of the subject. The part of the sun's disk not occu- 
pied by spots is far from uniformly bright. Its ground is 
finely mottled with an appearance of minute, dark dots, 
or pores, which, when attentively watched, are found to 



14 Mayer, Obs. Mar. 15, 1758. "Ingens macula in sole conspiciebatur, 
cujus diameter — jj> diam. solis. " 

16 Half the sun's disk is said in certain ancient annals to have been obscured 
by spots. This is monstrous — but on at least two occasions before the invention 
of telescopes spots have been seen with the naked eye. M. Gautier (Bibl. Univ. 
de Geneve, July and Aug., 1852) mentions as one of the largest spots on record, 
that observed by Sir W. Herschel, in 1779, which he there states to have been 
470" in diameter, or 15 '7 times that of the earth. I have not been able to verify 
the citation. The great spot of 1779 mentioned by Sir W. H. (Phil. Tr. 1795) 
as having been seen with the naked eye, consisted he says, of two parts, the 
largest of which "measured 1' 8" -06 in diameter, which is equal in length to 
more than 31000 miles." "Both together," he adds, "must certainly have 
extended above 50000." This corresponds to 113" which is not a fourth part 
of M. Gautier's quantity; moreover, 470" on the sun's disk corresponds, not to 
15-7, but to 27*3 diameters of the earth. — {Note added in 1858.) 



OUTLINES OF ASTRONOMY 313 

be in a constant state of change. There is nothing which 
represents so faithfully this appearance as the slow sub- 
sidence of some flocculent chemical precipitates in a trans- 
parent fluid, when viewed perpendicularly from above: so 
faithfully, indeed, that it is hardly possible not to be im- 
pressed with the idea of a luminous medium intermixed, 
but not confounded, with a transparent and non-luminous 
atmosphere, either floating as clouds in our air, or per- 
vading it in vast sheets and columns like flame, or the 
streamers of our northern lights, directed in lines perpen- 
dicular to the surface. 18 [See § 387 a, 6, and cc, Note Gr.] 
(388.) Lastly, in the neighborhood of great spots, or ex- 



16 The light emanating immediately from the sun shows no sign of polariza- 
tion whether radiating from the central or circumferential portions of its disk. 
This has been adduced as affording a direct experimental proof of the gaseous 
nature of the surface from which its light proceeds. It is argued that the light 
emitted by incandescent solid or fluid terrestrial bodies at great obliquities to 
their surfaces, is always found to be partially polarized in a plane perpendicular 
to that in which the angle of emanation lies, and that consequently such cannot 
be the nature of the solar surface. In former editions of this work, I have 
passed this argument sub silentio, and should not have thought it necessary now 
to enter a protest against its validity (resting as it does on authority of one of 
the greatest names in optical science), but that I find it prominently put forward 
and repeated and strongly insisted on in recent works of conspicuous merit. 
(Kosmos, passim, especially vol. iii. pp. 47, 284, and notes 99, 483, transl. ; 
Gautier on the Sun, Bibl. Univ. 1852 ; Vaughan, Rep. Brit. Assoc. 1857 ; Athe- 
naeum, No. 1560, etc.) The fallacy consists in the assumption that the surface 
from which the light emanates at the borders of the sun is necessarily very 
oblique to the visual ray by which we see it ; which, though true of the general 
surface regarded as a portion of a sphere 880,000 miles in diameter, is not so of 
each particular square foot or square inch which, not being obscured from sight 
by intervening protuberances, may send out rays to reach the eye of a terres- 
trial spectator. Supposing the sun to be an incandescent solid not more rough 
than the earth or the moon, it is obvious that whether from the centre or from 
the borders, the light by which we see it must consist of a mixture of rays 
emergent from the local surface at every possible angle of obliquity and in every 
possible plane without the smallest preference. A luminous portion of the sun's 
surface occupying the ten thousandth part of a square second, would correspond 
to a sectional area of the visual beam upward of twenty square miles in extent, 
admitting every variety of plain, precipice, slope, or rugged ground. The gen- 
eral surface of a forest seen on the horizon is parallel to the mathematical hori- 
zon, but who would assert that the ray by which its extreme visible leaf is seen, 
necessarily emanates from that leaf at any one obliquity or in any one plane of 
emergence rather than any other? — (Note added in 1858.) 
Astronomy — Vol. XIX— 14 



314 OUTLINES OF ASTRONOMY 

tensive groups of them, large spaces of the surface are often 
observed to be covered with strongly marked curved or 
branching streaks, more luminous than the rest, called 
faculce, and among these, if not already existing, spots 
frequently break out. They may, perhaps, be regarded 
with most probability as the ridges of immense waves in 
the luminous regions of the sun's atmosphere, indicative 
of violent agitation in their neighborhood. They are most 
commonly, and best seen, toward the borders of the visible 
disk, and their appearance is as represented in Plate I. fig. 1. 
(389.) But what are the spots? Many fanciful notions 
have been broached on this subject, but only one seems to 
have any degree of physical probability, viz. that they are 
the dark, or at least comparatively dark, solid body of the 
sun itself, laid bare to our view by those immense fluctua- 
tions in the luminous regions of its atmosphere, to which it 
appears to be subject. Respecting the manner in which 
this disclosure takes place, different ideas again have been 
advocated. Lalande (art. 3240) suggests, that eminences in 
the nature of mountains are actually laid bare, and project 
above the luminous ocean, appearing black above it, while 
their shoaling declivities produce the penumbras, where the 
luminous fluid is less deep. A fatal objection to this theory 
is the uniform shade of the penumbra and its sharp termina- 
tion, both inward, where it joins the spot, and outward, 
where it borders on the bright surface. A more probable 
view has been taken by Sir William Herschel, 17 who con- 
siders the luminous strata of the atmosphere to be sustained 
far above the level of the solid body by a transparent elastic 
medium, carrying on its upper surface (or rather, to avoid 

« PhiL Trans. 1801. 




OUTLINES OP ASTRONOMY 315 

the former objection, at some considerably lower level within 
its depth) a cloudy stratum which, being strongly illumi- 
nated from above, reflects a con- 
siderable portion of the light to 
our eyes, and forms a penumbra, 
while the solid body shaded by 
the clouds reflects none. (See fig.) 
The temporary removal of both 
the strata, but more of the upper 
than the lower, he supposes ef- 
fected by powerful upward cur- 
rents of the atmosphere, arising, perhaps, from spiracles 
in the body, or from local agitations. 

(389 a.) Such was the state of our knowledge of the ap- 
pearance and constitution of the solar spots at the time when 
this work first issued from the press. But in 1851, a further 
step toward penetrating the mystery of their nature was 
made by that excellent and indefatigable observer Mr. 
Dawes, who availing himself of the ingenious contrivance 
described in art. 204 e, has been enabled to scrutinize the 
interior of the penumbrse of the spots, under high magnify- 
ing powers, in perfect security and with all the advantage 
which the absence of extraneous glare confers on the exami- 
nation of feebly illuminated objects. So viewed, he has 
found the blacker portions occupying the middle of the 
penumbra, and which to former observers appeared so dark 
and so uniform as to lead them to believe it to be the sun's 
actual surface seen through an aperture in an exterior en- 
velope — to be, itself, only an additional and inferior stratum 
of very feebly luminous (or illuminated) matter, which he 
has called "the cloudy stratum," which again in its turn is 
frequently seen to be pierced with a smaller and usually 



816 OUTLINES OF ASTRONOMY 

much more rounded aperture, which would seem at length 
to afford a view of the real solar surface of most intense 
blackness. Figs. 4, 5, Plate L, represent spots so seen on 
23d December, 1851, and 17th January, 1852. In tracing 
the changes in the spots, from day to day, Mr. Dawes has 
also been led to conclude, that, in many instances, they 
have a movement of rotation about their own centres. This 
was particularly remarkable in the spot of 17th January, 
which between that date and 23d January had revolved in 
its own plane through an angle of more than 90°; the 
"cloudy stratum," which its central aperture, presenting 
itself under the aspect represented at b fig, 5, instead of 
that at a, which it originally had, its general form remain- 
ing all the while unchanged. 

(390.) When the spots are attentively watched, their 
situation on the disk of the sun is observed to change. 
They advance regularly toward its western limb or border, 
where they disappear, and are replaced by others which 
enter at the eastern limb, and which, pursuing their respec- 
tive courses, in their turn disappear at the western. The 
apparent rapidity of this movement is not uniform, as it 
would be were the spots dark bodies passing, by an inde- 
pendent motion of their own, between the earth and the 
sun; but is swiftest in the middle of their paths across 
the disk, and very slow at its borders. This is precisely 
what would be the case supposing them to appertain to and 
make part of the visible surface of the sun's globe, and to 
be carried round by a uniform rotation of that globe on its 
axis, so that each spot should describe a circle parallel to 
the sun's equator, rendered elliptic by the effect of perspec- 
tive. Their apparent paths also across the disk conform to 
this view of their nature, being, generally speaking, ellipses, 



OUTLINES OF ASTRONOMY 317 

much elongated, concentric with the sun's disk, each having 
one of its chords for its longer axis, and all these axes 
parallel to each other. At two periods of the year only do 
the spots appear to describe straight lines, viz. on and near 
to the 4th of June and 5th of December, on which days, 
therefore, the plane of the circle, which a spot situated on 
the sun's equator describes (and consequently, the plane 
of that equator itself), passes through the earth. Hence it 
is obvious, that the plane of the sun's equator is inclined to 
that of the ecliptic, and intersects it in a line which passes 
through the place of the earth on these days. The situation 
of this line, or the line of the nodes of the sun's equator as it 
is called, is, therefore, denned by the longitudes of the 
earth as seen from the snn at those epochs, which, accord- 
ing to Mr. Carrington, are respectively 73° 40' and 253° 
40' (=73° 40'+180°) for 1850, being, of course, diametrically 
opposite in direction. 

(391.) The inclination of the sun's axis (that of the plane 
of its equator) to the ecliptic is determined by ascertaining 
the proportion of the longer and the shorter diameter of the 
apparent ellipse described by any remarkable, well- denned 
spot; in order to do which, its apparent place on the sun's 
disk must be very precisely ascertained by micrometric 
measures, repeated from day to day as long as it continues 
visible (usually about 12 or 13 days, according to the mag- 
nitude of the spots, which always vanish by the effect of 
foreshortening before they attain the actual border of the 
disk — but the larger spots being traceable closer to the limb 
than the smaller 18 ). The reduction of such observations, or 



18 The great spot of December, 1719, is stated to have been seen as a notch 
in the limb of the sun. 



518 



OUTLINES OF ASTRONOMY 



the conclusion from them of the element in question, is 
complicated with the effect of the earth's motion in the 
interval of the observations, and with its situation in the 
ecliptic, with respect to the line of nodes. For simplicity, 
we will suppose the earth situated as it is on the 4th of 
March, in a line at right angles to that of the nodes, i.e. 
in the heliocentric longitude 163° 40', and to remain there 
stationary during the whole passage of a spot across the 
disk. In this case the axis of rotation of the sun will be 
situated in a plane passing through the earth and at right 



b A la ■ 



angles to the plane of the ecliptic. Suppose C to represent 
the sun's centre, P p its axis, E C the line of sight, P 1ST Q 
ApSa section of the sun passing through the earth, and 
Q a spot situated on its equator, and in that plane, and con- 
sequently in the middle of its apparent path across the disk. 
If the axis of rotation were perpendicular to the ecliptic, as 
N S, this spot would be at A, and would be seen projected 
on C, the -centre of the sun. It is actually at Q, projected 
upon D, at an apparent distance D to the north of the 
centre, which is the apparent smaller semi-axis of the ellipse 



OUTLINES OF ASTRONOMY 319 

described by the spot, which being known by micrometric 

C D 

measurement, the value of p^= or the cosine of Q C N, the 

inclination of the sun's equator becomes known, C K being 
the apparent semi-diameter of the sun at that time. At this 
epoch, moreover, the northern half of the circle described 
by the spot is visible (the southern passing behind the body 
of the sun), and the south pole p of the sun is within the 
visible hemisphere. This is the case in the whole interval 
from December 5th to June 4th, during which the visual 
ray falls upon the southern side of the sun's equator. The 
contrary happens in the other half year, from June 4th to 
December 5th, and this is what is understood when we say 
that the ascending node (denoted &) of the sun's equator 
lies in 73° 40' longitude — a spot on the equator passing that 
node being then in the act of ascending from the southern 
to the northern side of the plane of the ecliptic — such being 
the conventional language of astronomers in speaking of 
these matters. 

(392.) If the observations are made at other seasons 
(which, however, are the less favorable for this purpose 
the more remote they are from the epochs here assigned); 
when, moreover, as in strictness is necessary, the motion 
of the earth in the interval of the measures is allowed for 
(as for a change of the point of sight); the calculations req- 
uisite to deduce the situation of the axis in space, and the 
duration of the revolution around it, become much more 
intricate, and it would be beyond the scope of this work 
to enter into them 19 According to Mr. Carrington's deter- 



19 See the theory in Lalande's Astronomy, art. 3258, and the formula of 
computation in a paper by Petersen, Schumacher's Nachrichten, No. 419. 



320 OUTLINES OF ASTRONOMY 

mination, the inclination of the sun's equator to the ecliptic 
is about 7° 15' (its nodes being as above stated), and the 
period of rotation 25 days 9 hours 7 minutes; the corre- 
sponding synodic period being 27 days 6 hours 36 minutes. 20 

(393.) The region of the spots is confined, generally 
speaking, within about 25° on either side of the sun's 
equator; beyond 30° they are very rarely seen; in the 
polar regions, never. The actual equator of the sun is 
also less frequently visited by spots than the adjacent 
zones on either side, and a very material difference in 
their frequency and magnitude subsists in its northern and 
southern hemisphere, those on the northern preponderating 
in both respects. The zone comprised between the 11th 
and 15th degree to the northward of the equator is partic- 
ularly fertile in large and durable spots. These circum- 
stances, as well as the frequent occurrence of a more or 
less regular arrangement of the spots, when numerous, in 
the manner of belts parallel to the equator, point evidently 
to physical peculiarities in certain parts of the sun's body 
more favorable than in others to the production of the 
spots, on the one hand; and on the other, to a general 
influence of its rotation on its axis as a determining cause 
of their distribution and arrangement, and would appear 
indicative of a system of movements in the fluids which 
constitute its luminous surface bearing no remote analogy 
to our trade winds — from whatever cause arising. (See art. 
239 et seq.) 

(394.) The duration of individual spots is commonly not 



20 These periods are those of a spot in heliographic latitude 15° N. or S. of 
the sun's equator. Owing to solar atmospheric drift, the periods of rotation 
deduced from observations of spots in high or low heliographic latitudes differ 
considerably. [See Note G, § 38f c c] 



OUTLINES OF ASTRONOMY 821 

great; some are formed and disappear within the limit of 
a single transit across the disk — but such are for the most 
part small and insignificant. Frequently they make one or 
two revolutions, being recognized at their reappearance by 
their situation with respect to the equator, their configura- 
tions inter se, their size, or other peculiarities, as well as 
by the interval elapsing between their disappearance at one 
limb and reappearance on the other. In a few rare cases, 
however, they have been watched round many revolutions. 
The great spot of 1779 appeared during six months, ana 
one and the same groupe was observed in 1840 by Schwabe 
to return eight times." It has been surmised, with consid- 
erable apparent probability, that some spots, at least, are 
generated again and again, at distant intervals of time, over 
the same identical points of the sun's body (as hurricanes, 
for example, are known to affect given localities on the 
earth's surface, and to pursue definite tracks). The uncer- 
tainty which still prevails with respect to the exact duration 
of its rotation renders it very difficult to obtain convincing 
evidence of this; nor, indeed, can it be expected, until by 
bringing together into one connected view the recorded 
state of the sun's surface during a very long period of 
time, and comparing together remarkable spots which have 
appeared on the same parallel, some precise periodic time 
shall be found which shall exactly conciliate numerous and 
well-characterized appearances. The inquiry is one of sin- 
gular interest, as there can be no reasonable doubt that the 
supply of light and heat afforded to our globe stands in 
intimate connection with those processes which are taking 



81 Schum. Nach. No. 418, p. 150. The recent papers of Biela, Capocci, 
Schwabe, Pastorff and Schmidt, in that collection, will be found highly inter- 
esting. 



522 OUTLINES OF ASTRONOMY 

place on the solar surface, and to which the spots in some 
way or other owe their origin. 

(394 a.) Meanwhile M. Schwabe, of Dessau, by compar- 
ing together the records of the general state of the sun's 
surface in respect of the abundance and paucity of spots 
exhibited by it from 1826 to 1850, has been led to a highly 
remarkable conclusion, viz. that their degree of copious- 
ness is subject to a law of periodicity; alternate minima 
and maxima recurring at nearly equal intervals. The in- 
terval from minimum to minimum, as well as could be 
ascertained from the moderate interval embraced by the 
observations compared, was provisionally estimated by M. 
Schwabe at about ten years. More recently, M. Wolf, of 
Berne, 33 from a careful assemblage and discussion of all the 
recorded observations of spots which could be collected 
from their first telescopic discovery (by Fabricius and Har- 
riot, in 1610) to the present time, while fully confirm- 
ing their periodicity, has fixed upon the somewhat longer 
period, from minimum to minimum, of ll y *ll, being ex- 
actly at the rate of nine periods per century, the last year 
of each century (1700, 1800, etc.) being a year of minim am. 
In the minima there is for the most part an extreme pau- 
city, and sometimes an entire absence of spots. 33 The max- 
ima (in which they are often so copious that 50 or 100 have 
been counted at once on the disk) do not appear to fall ex- 
actly in the middle year between the minima, but rather 
earlier, about the fifth, fourth, or even the third year of 
the period. What is extremely remarkable, and must cer- 
tainly be received as strongly corroborative, both of the 



99 Rudolf Wolf. Transactions of Society of Nat. Phil. Berne. 1852. 
93 As in 1856. 



OUTLINES OF ASTRONOMY 323 

general fact of periodicity and of the correctness of M. 
Wolf's period, is, that we find recorded in history by 
chroniclers and annalists on several occasions before the 
invention of telescopes, the appearance of spots, or groups 
of spots, so considerable as to have become matter of vulgar 
observation, as for instance in the years A.D. 807, 840, 1096 
and 1607, a4 and several others in which, though no spots are 
recorded, a great deficiency in the sun's light has been re- 
marked. Thus in the annals of the year A.D. 536, the sun 
is said to have suffered a great diminution of light, which 
continued fourteen months. From October, A.D. 626, to the 
following June, a defalcation of light to the extent of one- 
half is recorded; and in A.D. 1547, during three days, the 
sun is said to have been so darkened that stars were seen 
in the day time. Now of all these instances, supposing 
them all to have been owing to spots, either unusually 
large or numerous, there are only two, those of A.D. 807 
and 1607, which deviate so much as two years from the 
epochs of maximum fixed as above. 

(394 b.) Sir W. Herschel (Ph. Tr. 1801), considering the 
appearance of abundant spots on the sun's disk as evidence 
of an agitated state of its gaseous envelope, and regarding 
the extrication of light and heat as the results of chemical 
processes likely to be promoted by the more intimate mix- 
ture of heterogeneous materials having mutual affinities, 
has attempted to show, though from very imperfect records 
(such as alone could be procured by him at that date) that 
years of remarkably abundant or deficient spots have been 
also remarkable respectively for their high or low general 



24 Those spots were taken for planets seen on the sun; that of 840 for 
Venus; those of 807 and 1607 for Mercury. 



324 OUTLINES OF ASTRONOMY 

temperature, and especially for abundant and deficient har- 
vests. The point has been inquired into by M. G-autier," 
who from an assemblage of meteorological averages ob- 
tained in thirty-three stations in Europe, and twenty-nine 
in America during eleven years of observation, finds a 
trifling preponderance (0 o, ll Fahr.) in the opposite direc- 
tion. On the other hand M. Wolf, in the memoir above 
cited, from an examination of the Chronicles of Zurich 
from the year A.D. 1000 to A.D. 1800, is led to a conclusion 
in accordance with this speculation, and considers them as 
affording decisive evidence "that years rich in solar spots 
are in general drier and more fruitful than those of an oppo- 
site character, while the latter are wetter and more stormy 
than the former." 

(394 c.) Although more properly belonging to the do- 
main of general physics than of astronomy, it is impossi- 
ble to omit mentioning here the singular coincidence of this 
period of the recurrence of the solar spots with that of those 
great disturbances in the magnetic system of the earth to 
which the epithet of "magnetic storms" has been affixed. 
These disturbances, during which the magnetic needle is 
greatly and universally agitated (not in a particular limited 
locality, but at one and the same instant of time over whole 
continents, or even over the whole earth), are found, so far 
as observation has hitherto extended, to maintain a parallel 
both in respect of their frequency of occurrence and inten- 
sity in successive years with the abundance and magnitude 
of the spots in the same years, too close to be regarded as 
fortuitous. The coincidence of the epochs of maxima and 
minima in the two series of phenomena amounts indeed to 

25 Bibl. Univ. de Geneve. 1844. 



OUTLINES OF ASTRONOMY 325 

identity, a fact evidently of most important significance, 
but which neither astronomical nor magnetic science is yet 
sufficiently advanced to interpret. 

(395.) Above the luminous surface of the sun, and the 
region in which the spots reside, there are strong indications 
of the existence of a gaseous atmosphere having a somewhat 
imperfect transparency. When the whole disk of the sun 
is seen at once through a telescope magnifying moderately 
enough to allow it, and with a darkening glass such as to 
suffer it to be contemplated with perfect comfort, it is very 
evident that the borders of the disk are much less luminous 
than the centre. That this is no illusion is shown by pro- 
jecting the sun's image undarkened and moderately magni- 
fied, so as to occupy a circle two or three inches in diameter, 
on a sheet of white paper, taking care to have it well in 
focus, when the same appearance will be observed. 86 This 
can only arise from the circumferential rays having under- 
gone the absorptive action of a much greater thickness of 
some imperfectly transparent envelope (due to greater ob- 
liquity of their passage through it) than the central. — But a 
still more convincing and indeed decisive evidence is offered 
by the phenomena attending a total eclipse of the sun. 
Such eclipses (as will be shown hereafter) are produced by 
the interposition of the dark body of the moon between the 
earth and sun, the moon being large enough to cover and 



86 This has been denied by Arago on the evidence of certain phenomena 
observed with his "polariscope" ; but the fact is so palpable, that it is matter of 
some astonishment that it could ever fail to strike the most superficial observer. 
The matter has been placed beyond a doubt, however, by direct experiments 
both photometric and thermic. The details of the latter by Sig. Secchi will be 
found in Astron. Nashr. Nob. 806, 833, and go to prove that the calorific radia- 
tion of the centre of the sun's disk is nearly double of that from its borders, 
and that the equatorial regions are somewhat hotter than the polar (Comptes 
Rendus, Aug. 26, 1852).— Note added 1858. 



S26 OUTLINES OF ASTRONOMY 

surpass, by a very small breadth, the whole disk of the sun. 
Now when this takes place, were there no vaporous atmos- 
phere capable of reflecting any light about the sun, the sky 
ought to appear totally dark, since (as will hereafter abun- 
dantly appear) there is not the smallest reason for believing 
the moon to have any atmosphere capable of doing so. So 
far, however, is this from being the case, that a bright ring 
or corona of light is seen, fading gradually away, as rep- 
resented in Plate 1. fig. 3, which (in cases where the moon 
is not centrally superposed on the sun) is observed to be con- 
centric with the latter, not the former body. This corona was 
beautifully seen in the eclipse of July 7, 1842, and with this 
most remarkable addition—witnessed by every spectator in 




Pa via, Milan, Vienna, and elsewhere: three distinct and 
very conspicuous rose-colored protuberances (as represented 
in the figure cited) were seen to project beyond the dark 
limb of the moon, likened by some to flames, by others to 
mountains, but which their enormous magnitude (for to have 
been seen at all by the naked eye their height must have 
exceeded 40,000 miles), and their faint degree of illumina- 
tion, clearly prove to have been cloudy masses of the most 
excessive tenuity, and which doubtless owed their support, 
and probably their existence, to such an atmosphere as we 
are now speaking of. In the total eclipse of July 28, 1851, 
similar rose-colored protuberances were observed, one in 
particular of a form quite decisive as to their cloudy nature, 
rising straight up vertically from the edge of the disk, and 



OUTLINES OF ASTRONOMY 327 

then suddenly turning off at a right angle (as in the annexed 
figure, which represents the appearance as seen by Prof. 
Schmidt, at Eastenburg), just as a column of smoke rising 
in calm air is often seen to be drifted off horizontally when 
it has attained such a height as to bring it into an upper cur- 
rent of wind. To complete the resemblance, a detached and 
perfectly insulated mass B of the same rosy color was ob- 
served at some distance from the drifted train A, which was 
connected with another mass C, by a narrow red band or 
streak D. 

(395 a.) The existence of such an atmosphere superior to 
the luminous envelope being admitted, affords an easy ex- 
planation of the faculse, considered as vast waves in the 
photosphere (art. 388). In an atmosphere consisting of 
strata gradually decreasing in density, any cause of undu- 
lation acting on the inferior strata will throw them up to 
a vastly greater height, and therefore produce far greater 
waves in them than would arise from the same cause act- 
ing on the surface of a definite ocean of liquid matter, by 
reason of their being partially sustained against gravity, 
leaving their inertia free to carry them up to a higher level. 
The experiment is easily tried in oil floating on water, or in 
saline solutions increasing in density downward, and is at 
once amusing and instructive. [See Note O, § 395 b 5.] 

(396.) That the temperature at the visible surface of the 
sun cannot be otherwise than very elevated, much more so 
than any artificial heat produced in our furnaces, or by chem- 
ical or galvanic processes, we have indications of several 
distinct kinds: 1st, From the law of decrease of radiant heat 
and light, which, being inversely as the squares of the dis- 
tances, it follows, that the heat received on a give", area ex- 
posed at the distance of the earth, and on an equal area at 



328 OUTLINES OF ASTRONOMY 

the visible surface of the sun, must be in the proportion of 
the area of the sky occupied by the sun's apparent disk 
to the whole hemisphere, or as 1 to about 92,000. A far 
less intensity of solar radiation, collected in the focus of a 
burning-glass, suffices to dissipate gold and platina in vapor. 
2dly, From the facility with which the calorific rays of the 
sun traverse glass, a property which is found to belong to 
the heat of artificial fires in the direct proportion of their 
intensity." 3dly, From the fact, that the most vivid flames 
disappear, and the most intensely ignited solids appear only 
as black spots on the disk of the sun when held between it 
and the eye. 28 From the last remark it follows, that the 
body of the sun, however dark it may appear when seen 
through its spots, may, nevertheless, be in a state of most 
intense ignition. It does not, however, follow of necessity 
that it must be so. The contrary is at least physically 
possible. A perfectly reflective canopy would effectually 
defend it from the radiation of the luminous regions above 
its atmosphere, and no heat would be conducted downward 
through a gaseous medium increasing rapidly in density. 
That the penumbral clouds are highly reflective, the fact 
of their visibility in such a situation can leave no doubt. 
(397.) As the magnitude of the sun has been measured, 
ancf (as we shall hereafter see) its weight, or quantity of pon- 

27 By direct measurement with the actinometer, I find that out of 1,000 
calorific solar rays, 816 penetrate a sheet of plate glass 0'12 inch thick; and 
that of 1,000 rays which have passed through one such plate, 859 are capable 
of passing through another. H. 182 *l. 

28 The ball of ignited quicklime, in Lieutenant Drummond's oxy -hydrogen 
lamp, gives the nearest imitation of the solar splendor which has yet been pro- 
duced. The appearance of this against the sun was, however, as described in 
an imperfect trial at which I was present. The experiment ought to be re- 
peated under favorable circumstances. — Note to the ed. of ]833. According 
to the more recent experiments of Messrs. Pizeau and Poucault, the intensity of 
the fight at the surface of Drummond's lime-ball is only one-146th part of that 
at the surface of the sun! — Note added 1858. 



OUTLINES OF ASTRONOMY 329 

derable matter, ascertained, so also attempts have been 
made, and not wholly without success, from the heat actu- 
ally communicated by its rays to given surfaces of material 
bodies exposed to their vertical action on the earth's sur- 
face, to estimate the total expenditure of heat by that lumi- 
nary in a given time. The result of such experiments has 
been thus announced. Supposing a cylinder of ice 45 miles 
in diameter to be continually darted into the sun with the 
velocity of light, and that the water produced by its fusion 
were continually carried off, the heat now given off con- 
stantly by radiation would then be wholly expended in its 
liquefaction, on the one hand, so as to leave no radiant 
surplus; while on the other, the actual temperature at its 
surface would undergo no diminution. 29 

(397 a.) Another mode of expressing the heat generated 
and radiated off from the sun's surface, well calculated to 
impress us with an overwhelming idea of the tremendous 
energies there constantly in action, is that employed by Pro- 
fessor Thomson, who estimates the dynamical effect which 
would be produced in our manufactories by a consumption 
of fuel competent to evolve the heat given out by each indi- 
vidual square yard of that surface, at 63000 horse-power, to 
maintain which would require the combustion of 13500 
pounds of coal per hour. 80 



29 "Results of Astronomical Observations at the Cape of Good Hope," 
p. 444. 

30 See Trans. R. S. Edin. xxi. p. 69. "On the Mechanical Energies of the 
Solar System," by Sir W. Thomson, Prof. Nat. Phil., Glasgow. The Professor 
grounds this estimate on M. Pouillet's determination of the amount of solar 
radiation and Mr. Joule's estimate of the mechanical equivalent of a centigrade 
thermal unit. The author of this work found at the Cape of Good Hope, by 
experiments made on six summer days, from December 23, 1836, to January 
9, 1837, the sun being nearly vertical in each experiment, that in that latitude 
at midsummer, at noon, and at 140 feet above the sea level, the solar radiation 
is competent to melt an inch in thickness from a sheet of ice exposed perpendic- 
ularly to its rays (if wholly so employed) in 2h. 12m. 42s. Estimating the heat 



830 OUTLINES OF ASTRONOMY 

(398.) This immense escape of heat by radiation, we may 
remark, will fully explain the constant state of tumultuous 
agitation in which the fluids composing the visible surface 
are maintained, and the continual generation and filling in 
of the pores, without having recourse to internal causes. 
The mode of action here alluded to is perfectly represented 
to the eye in the disturbed subsidence of a precipitate, as 
described in art. 387, when the fluid from which it subsides 
is warm, and losing heat from its surface. 

(399.) The sun's rays are the ultimate source of almost 
every motion which takes place on the surface of the earth. 
By its heat are produced all winds, and those disturbances 
in the electric equilibrium of the atmosphere which give rise 
to the phenomena of lightning, and probably also to those 
of terrestrial magnetism and the aurora. By their vivifying 
action vegetables are enabled to draw support from inor- 
ganic matter, and become, in their turn, the support of ani- 
mals and of man, and the sources of those great deposits of 
dynamical efficiency which are laid up for human use in our 
coal strata. 31 By them the waters of the sea are made to cir- 
culate in vapor through the air, and irrigate the land, pro- 
ducing springs and rivers. By them are produced all dis- 
turbances of the chemical equilibrium of the elements of 
nature, which, by a series of compositions and decomposi- 
tions, give rise to new products, and originate a transfer of 
materials. Even the slow degradation of the solid constitu- 



absorbed in traversing our atmosphere at one-third of the total quantity incident 
on it, this gives, all reductions made, 43 '39 feet in thickness of ice per minute 
melted at the sun's surface. M. Pouillet's experiments (made in June, 183V), 
give 11-80 metres or 38*7 feet per minute. Forty feet may therefore be taken 
as a probable mean, and from this the result in art. 397 is calculated. 

81 So in the edition of 1833. The celebrated engineer StepTienson is gen- 
erally, but erroneously, cited as the originator of this remark. 



OUTLINES OF ASTRONOMY 331 

ents of the surface, in which its chief geological changes 
consist, is almost entirely due, on the one hand, to the abra- 
sion of wind and rain, and the alternation of heat and frost; 
on the other, to the continual beating of the sea waves, agi- 
tated by winds, the results of solar radiation. Tidal action 
(itself partly due to the sun's agency) exercises here a com- 
paratively slight influence. The effect of oceanic currents 
(mainly originating in that influence), though slight in abra- 
sion, is powerful in diffusing and transporting the matter 
abraded ; and when we consider - the immense transfer of 
matter so produced, the increase of pressure over large 
spaces in the bed of the ocean, and diminution over corre- 
sponding portions of the land, we are not at a loss to per- 
ceive how the elastic power of subterranean fires, thus 
repressed on the one hand and relieved on the other, may 
break forth in points where the resistance is barely adequate 
to their retention, and thus bring the phenomena of even 
volcanic activity under the general law of solar influence. 38 
(400.) The great mystery, however, is to conceive how 
so enormous a conflagration (if such it be) can be kept 
up. Every discovery in chemical science here leaves us 
completely at a loss, or rather, seems to remove further 
the prospect of probable explanation. If conjecture might 
be hazarded, we should look rather to the known possi- 
bility of an indefinite generation of heat by friction, or to 
its excitement by the electric discharge, than to any actual 
combustion of ponderable fuel, whether solid or gaseous, 
for the origin of the solar radiation. 33 Photographic repre- 

32 So in the edition of 1833. 

33 Electricity traversing excessively rarefied air or vapors gives out light, 
and, doubtless, also heat. May not a continual current of electric matter be 
constantly circulating in the sun's immediate neighborhood, or traversing the 
planetary spaces, and exciting, in the upper regions of its atmosphere, those 



332 OUTLINES OF ASTRONOMY 

sentations. of the spots have been made with much success 
by Mr. De la Eue, with a "photohelioscope" at Kew: also 
by the Rev. W. Selwyn, Canon of Ely, etc. 



phenomena of which, on however diminutive a scale, we have yet an unequivo- 
cal manifestation in our aurora borealis. The possible analogy of the solar light 
to that of the aurora has been distinctly insisted on by the late Sir W. Herschel, 
in his paper already cited. It would be a highly curious subject of experimental 
inquiry, how far a mere reduplication of sheets of flame, at a distance one behind 
the other (by which their light might be brought to any required intensity), 
would communicate to the heal of the resulting compound ray the penetrating 
character which distinguishes the solar calorific rays. We may also observe that 
the tranquillity of the sun's polar, as compared with its equatorial regions (if its 
spots be really atmospheric), cannot be accounted for by its rotation on its axis 
only, but must arise from some cause external to the luminous surface of the 
sun, as we see the belts of Jupiter and Saturn, and our trade winds, arise from 
a cause external to these planets, combining itself with their rotation, which 
alone can produce no motions when once the form of equilibrium is attained. 

The prismatic analysis of the solar beam exhibits in the spectrum a series 
of * 'fixed lines," totally unlike those which belong to the light of any known 
terrestrial flame. This may hereafter lead us to a clearer insight into its origin. 
But, before we can draw any conclusions from such an indication, we must 
recollect, that previous to reaching us it has undergone the whole absorptive 
action of our atmosphere, as well as of the sun's. Of the latter we know noth- 
ing, and may conjecture everything ; but of the blue color of the former we are 
sure; and if this be an inherent (i.e. an absorptive) color, the air must be ex- 
pected to act on the spectrum after the analogy of other colored media, which 
often (and especially light blue media) leave un absorbed portions separated by 
dark intervals. It deserves inquiry, therefore, whether some or all the fixed 
lines observed by Wollaston and Fraunhofer may not have their origin in our 
own atmosphere. Experiments made on lofty mountains, or the cars of bal- 
loons, on the one hand, and on the other with reflected beams which have been 
made to traverse several miles of additional air near the surface, would decide 
this point. The absorptive effect of the sun's atmosphere, and possibly also 
of the medium surrounding it (whatever it be) which resists the motions of 
comets, cannot be thus eliminated. — Note to the edition of 1833. The idea of 
referring the origin of the solar heat to friction has been worked out into an 
elaborate theory by Professor Thomson, in his paper already cited, of which 
some account will be given in a more advanced portion of this work. (1858.) 
The recent remarkable results of what is called "Spectrum Analysis" afford 
a curious commentary on this note. (1863.) [See note M. (1865.)] 



Note on Art. 394 a. — The year 1856 was remarkable for the absence of 
spots in the sun (in exact accordance with Wolf's period); during 1857 the 
phase of increased activity came on ; and the present year (1858) is ushered in 
with a magnificent display of spots in the sun's southern hemisphere. — Note 
added Jan. 4. 1858. 



OUTLINES OF ASTRONOMY 333 



CHAPTEE VII 

Of the Moon — Its Sidereal Period — Its Apparent Diameter — Its Parallax 
Distance, and Real Diameter — First Approximation to its Orbit — An 
Ellipse about the Earth in the Focus — Its Excentricity and Inclina- 
tion — Motion of its Nodes and Apsides — Of Occultations and Solar 
Eclipses Generally — Limits within which they are Possible — They 
Prove the Moon to be an Opaque Solid — Its Light Derived from the 
Sun — Its Phases — Synodic Revolution or Lunar Month — Harvest 
Moon — Of Eclipses more Particularly — Their Phenomena — Their Pe- 
riodical Recurrence — Physical Constitution of the Moon — Its Moun- 
tains and other Superficial Features — Indications of former Yolcanic 
Activity — Its Atmosphere — Climate — Radiation of Heat from its Sur- 
face — Rotation on its own Axis — Libration — Appearance of the Earth 
from it — Probable Elongation of the Moon's Figure in the Direction of 
the Earth — Its Habitability not Impossible — Charts, Models and Pho- 
tographs of its Surface 

(401.) The moon, like the sun, appears to advance among 
the stars with a movement contrary to the general diurnal 
motion of the heavens, but much more rapid, so as to be 
very readily perceived (as we have before observed) by a few 
hours' cursory attention on any moonlight night. By this 
continual advance, which, though sometimes quicker, some- 
times slower, is never intermitted or reversed, it makes the 
tour of the heavens in a mean or average period of 27 d 7 h 43 m 
ll s, 5, returning, in that time, to a position among the stars 
nearly coincident with that it had before, and which would 
be exactly so, but for reasons presently to be stated. 

(402.) The moon, then, like the sun, apparently describes 
an orbit round the earth, and this orbit cannot be very dif- 
ferent from a circle, because the apparent angular diam- 



334 OUTLINES OF ASTRONOMY 

eter of the full moon is not liable to any great extent of 
variation. 

(403.) The distance of the moon from the earth is con- 
cluded from its horizontal parallax, which may be found 
either directly, by observations at remote geographical sta- 
tions, exactly similar to those described in art. 355, in the 
case of the sun, or by means of the phenomena called oc- 
cupations, from which also its apparent diameter is most 
readily and correctly found. From such observations it re- 
sults that the mean or average value of the moon's hori- 
zontal parallax is 57' 2"°325, 1 and the mean distance of the 
centre of the moon from that of the earth is 60*255 of the 
earth's equatorial radii, or about 238793 miles, taking with 
Mr. Adams 57' 2" -325 for the mean horizontal parallax. 
This distance, great as it is, is little more than one-fourth 
of the diameter of the sun's body, so that the globe of the 
sun would nearly twice include the whole orbit of the moon; 
a consideration wonderfully calculated to raise our ideas of 
that stupendous luminary! 

(404.) The distance of the moon's centre from an ob- 
server at any station on the earth's surface, compared with 
its apparent angular diameter as measured from that station, 
will give its real or linear diameter. Now, the former dis- 
tance is easily calculated when the distance from the earth's 
centre is known, and the apparent zenith distance of the 
moon also determined by observation; for if we turn to 
the figure of art. 339, and suppose S the moon, A the sta- 
tion, and C the earth's centre, the distance S C, and the 
earth's radius C A, two sides of the triangle ACS 



1 This result, recently arrived at by Mr. Adams, coincides almost precisely 
with that assigned by Henderson, viz. 51' 2" C 3L 



OUTLINES OF ASTRONOMY 335 

are given, and the angle CAS, which is the supplement 
of Z A S, the observed zenith distance, whence it is easy 
to find A S, the moon's distance from A. From such ob- 
servations and calculations it results, that the real diameter 
of the moon is 2160 miles, or about 0*2729 of that of the 
earth, whence it follows that, the bulk of the latter being 
considered as 1, that of the former will be 0*0204, or 
about i. The difference of the apparent diameter of the 
moon, as seen from the earth's centre and from any point 
of its surface, is technically called the augmentation of the 
apparent diameter, and its maximum occurs when the moon 
is in the zenith of the spectator. Her mean angular diam- 
eter, as seen from the centre, is 31' 7", and is always = 0*545 
X her horizontal parallax. 

(405.) By a series of observations, such as described in 
art. 403, if continued during one or more revolutions of the 
moon, its real distance may be ascertained at every point 
of its orbit; and if at the same time its apparent places in 
the heavens be observed, and reduced by means of its paral- 
lax to the earth's centre, their angular intervals will become 
known, so that the path of the moon may then be laid down 
on a chart supposed to represent the plane in which its orbit 
lies, just as was explained in the case of the solar ellipse 
(art. 349). Now, when this is done, it is found that, neg- 
lecting certain small, though very perceptible deviations 
of which a satisfactory account will hereafter be rendered, 
the form of the apparent orbit, like that of the sun, is 
elliptic, but considerably more excentric, the excentricity 
amounting to 0*05484 of the mean distance, or the major 
semi-axis of the ellipse, and the earth's centre being situ- 
ated in its focus 

(406.) The plane in which this orbit lies is not the 



336 OUTLINES OF ASTRONOMY 

ecliptic, however, but is inclined to it at an angle of 5° 8' 
48", which is called the inclination of the lunar orbit, and 
intersects it in two opposite points, which are called its 
nodes — the ascending node being that in which the moon 
passes from the southern side of the ecliptic to the northern, 
and the descending the reverse. The points of the orbit at 
which the moon is nearest to and furthest from, the earth, 
are called respectively its perigee and apogee, and the line 
joining them and the earth the line of apsides. 

(407.) There are, however, several remarkable circum- 
stances which interrupt the closeness of the analogy, which 
cannot fail to strike the reader, between the motion of the 
moon around the earth, and of the earth around the sun. 
In the latter case, the ellipse described remains, during a 
great many revolutions, unaltered in its position and dimen- 
sions; or, at least, the changes which it undergoes are not 
perceptible but in a course of very nice observations, which 
have disclosed, it is true, the existence of "perturbations," 
but of so' minute an order, that, in ordinary parlance, and 
for common purposes, we may leave them unconsidered. 
But this cannot be done in the case of the moon. Even 
in a single revolution, its deviation from a perfect ellipse is 
very sensible. It does not return to the same exact position 
among the stars from which it set out, thereby indicating a 
continual change in the plane of its orbit. And, in effect, 
if we trace by observation, from month to month, the point 
where it traverses the ecliptic, we shall find that the nodes of 
its orbit are in a continual state of retreat upon the ecliptic. 
Suppose O to be the earth, and A b a d that portion of the 
plane of the ecliptic which is intersected by the moon, in its 
alternate passages through it, from south to north, and vice 
versd; and let A B C D E F be a portion of the moon's 




OUTLINES OF ASTRONOMY 337 

orbit, embracing a complete sidereal revolution. Suppose 
it to set out from the ascending node, A; then, if the orbit 
lay all in one plane, passing through O, it would have a, 
the opposite point in the ecliptic, for its descending node; 
after passing which, it would again ascend at A. But, in 
fact, its real path carries it not to a, but along a certain 
curve, A B C, to C, a point in the ecliptic less than 180° 
distant from A; so that the angle A O 0, or the arc of 
longitude described between the ascending and the descend- 
ing node, is somewhat less than 
180°. It then pursues its course 
below the ecliptic, along the curve 
C D E, and rises again above it, 
not at the point c, diametrically 
opposite to C, but at a point E, 
less advanced in longitude. On the whole, then, the arc 
described in longitude between two consecutive passages 
from south to north, through the plane of the ecliptic, 
falls short of 360° by the angle A O E; or, in other 
words, the ascending node appears to have retreated in 
one lunation on the plane of the ecliptic by that amount. 
To complete a sidereal revolution, then, it must still go on 
to describe an arc, E F, on its orbit, which will no longer, 
however, bring it exactly back to A, but to a point some- 
what above it, or having north latitude. 

(408.) The actual amount of this retreat of the moon's 
node is about 3' 10" -64 per diem, on an average, and in a 
period of 6793*39 mean solar days, or about 18*6 years, the 
ascending node is carried round in a direction contrary to 
the moon's motion in its orbit (or from east to west) over 
a whole circumference of the ecliptic. Of course, in the 

middle of this period the position of the orbit must have 
Astronomy— Vol. XIX.— 15 



338 OUTLINES OF ASTRONOMY 

been precisely reversed from what it was at the beginning. 
Its apparent path, then, will lie among totally different 
stars and constellations at different parts of this period ; and 
this kind of spiral revolution being continually kept up, it 
will, at one time or other, cover with its disk every point 
of the heavens within that limit of latitude or distance from 
the ecliptic which its inclination permits; that is to say, a 
belt or zone of the heavens, of 10° 18' in breadth, having 
the ecliptic for its middle line. Nevertheless, it still re- 
mains true that the actual place of the moon, in conse- 
quence of this motion, deviates in a single revolution very 
little from what it would be were the nodes at rest. Sup- 
posing the moon to set out from its node A, its latitude, 
when it comes to F, having completed a revolution in longi- 
tude, will not exceed 8'; which, though small in a single 
revolution, accumulates in its effect in a succession of 
many: it is to account for, and represent geometrically, 
this deviation, that the motion of the nodes is devised. 

(409.) The moon's orbit, then, is not, strictly speaking, 
an ellipse returning into itself, by reason of the variation of 
the plane in which it lies, and the motion of its nodes. But 
even laying aside this consideration, the axis of the ellipse 
is itself constantly changing its direction in space, as has 
been already stated of the solar ellipse, but much more rap- 
idly; making a complete revolution, in the same direction 
with the moon's own motion, in 3232*5753 mean solar days, 
or about nine years, being about 3° of angular motion in a 
whole revolution of the moon. This is the phenomenon 
known by the name of the revolution of the moon's apsides. 
Its cause will be hereafter explained. Its immediate effect 
is to produce a variation in the moon's distance from the 
earth, which is not included in the laws of exact elliptic 



OUTLINES OF ASTRONOMY 339 

motion. In a single revolution of the moon, this variation 
of distance is trifling ; but in the course of many it becomes 
considerable, as is easily seen, if we consider that in four 
years and a half the position of the axis will be completely 
reversed, and the apogee of the moon will occur where the 
perigee occurred before. 

(410.) The best way to form a distinct conception of the 
moon's motion is to regard it as describing an ellipse about 
the earth in the focus, and, at the same time, to regard this 
ellipse itself to be in a twofold state of revolution ; 1st, in 
its own plane, by a continual advance of its axis in that 
plane; and 2dly, by a continual tilting motion of the plane 
itself, exactly similar to, but much more rapid than, that 
of the earth's equator produced by the conical motion of its 
axis, described in art. 317. 

(411.) As the moon is at a very moderate distance from 
us (astronomically speaking), and is in fact our nearest 
neighbor, while the sun and stars are in comparison im- 
mensely beyond it, it must of necessity happen, that at one 
time or other it must pass over and occult or eclipse every 
star and planet within the zone above described (and, as 
seen from the surface of earth, even somewhat beyond it, 
by reason of parallax, which may throw it apparently nearly 
a degree either way from its place as seen from the centre, 
according to the observer's station). Nor is the sun itself 
exempt from being thus hidden, whenever any part of the 
moon's disk, in this her tortuous course, comes to overlap 
any part of the space occupied in the heavens by that lumi- 
nary. On these occasions is exhibited the most striking and 
impressive of all the occasional phenomena of astronomy, an 
eclipse of the sun, in which a greater or less portion, or even 
in some rare conjunctures the whole, of its disk is obscured, 



340 OUTLINES OF ASTRONOMY 

and, as it were, obliterated, by the superposition of that of 
the moon, which appears upon it as a circularly -terminated 
black spot, producing a temporary diminution of daylight, 
or even nocturnal darkness, so that the stars appear as if 
at midnight. In other cases, when, at the moment that the 
moon is centrally superposed on the sun, it so happens that 
her distance from the earth is such as to render her angular 
diameter less than the sun's, the very singular phenomenon 
of an annular solar eclipse takes place, when the edge of 
the sun appears for a few minutes as a narrow ring of light 
projecting on all sides beyond the dark circle occupied by 
the moon in its centre. 

(412.) A solar eclipse can only happen when the sun and 
moon are in conjunction, that is to say, have the same, or 
nearly the same, position in the heavens, or the same longi- 
tude. It appears by art. 409 that this condition can only 
be fulfilled at the time of a new moon, though it by no 
means follows, that at every conjunction there must be an 
eclipse of the sun. If the lunar orbit coincided with the 
ecliptic, this would be the case, but as it is inclined to it 
at an angle of upward of 5°, it is evident that the conjunc- 
tion, or equality of longitudes, may take place when the 
moon is in the part of her orbit too remote from the ecliptic 
to permit the disks to meet and overlap. It is easy, how- 
ever, to assign the limits within which an eclipse is possi- 
ble. To this end we must consider, that, by the effect of 
parallax, the moon's apparent edge may be thrown in any 
direction, according to a spectator's geographical station, by 
any amount not exceeding her horizontal parallax, and the 
same holds good of the sun, so that there is a displacement 
to the extent of the difference of the two parallaxes. Now, 
this comes to the same (so far as the possibility of an eclipse 



OUTLINES OF ASTRONOMY 341 

is concerned) as if the apparent diameter of the moon, seen 
from the earth's centre, were dilated by twice the difference 
of their horizontal parallaxes ; for if, when so dilated, it can 
touch or overlap the sun, there must be an eclipse at some 
part or other of the earth's surface. If, then, at the mo- 
ment of the nearest conjunction, the geocentric distance of 
the centres of the two luminaries do not exceed the sum 
of their semidiameters and of the last-mentioned difference, 
there will be an eclipse. The sum is, at its maximum, 
about 1° 34' 26". In the spherical triangle SNM, then, 
in which S is the sun's centre, M the moon's, S N the 
ecliptic, M K the moon's orbit, and N the node, we may 
suppose the angle N S M a right angle, S M = 1° 34' 26", 
and the angle, M N S = 5° 8' 48", the inclination of the 
orbit. Hence we calculate S N, 
which comes out 16° 58'. If, then, 
at the moment of the new moon, the 
moon's node is further from the sun 
in longitude than this limit, there 
can be no eclipse ; if within, there may, and probably will, 
at some part or other of the earth. To ascertain precisely 
whether there will or not, and, if there be, how great will 
be the part eclipsed, the solar and lunar tables must be con- 
sulted, the place of the node and the semidiameters exactly 
ascertained, and the local parallax, and apparent augmenta- 
tion of the moon's diameter due to the difference of her 
distance from the observer and from the centre of the earth 
(which may amount to a sixtieth part of her horizontal 
diameter), determined; after which it is easy, from the 
above considerations, to calculate the amount overlapped 
of the two disks, and their moment of contact. 

(413.) The calculation of the occultation of a star de- 




342 OUTLINES OF ASTRONOMY 

pends on similar considerations. An occultation is possi- 
ble, when the moon's course, as seen from the earth's centre, 
carries her within a distance from the star equal to the sum 
of her semidiameter and horizontal parallax; and it will 
happen at any particular spot, when her apparent path, as 
seen from that spot, carries her centre within a distance 
equal to the sum of her augmented semidiameter and actual 
parallax. The details of these calculations, which are some- 
what troublesome, must be sought elsewhere. 3 

(414.) The phenomenon of a solar eclipse and of an oc- 
cultation are highly interesting and instructive in a physical 
point of view. They teach us that the moon is an opaque 
body, terminated by a real and sharply denned surface in- 
tercepting light like a solid. They prove to us, also, that 
at those times when we cannot see the moon, she really ex- 
ists, and pursues her course, and that when we see her only 
as a crescent, however narrow, the whole globular body is 
there, filling up the deficient outline, though unseen. For 
occultations take place indifferently at the dark and bright, 
the visible and invisible outline, whichever happens to be 
toward the direction in which the moon is moving; with 
this only difference, that a star occulted by the bright limb, 
if the phenomenon be watched with a telescope, gives no- 
tice, by its gradual approach to the visible edge, when to 
expect its disappearance, while, if occulted at the dark 
limb, if the moon, at least, be more than a few days old, 
it is, as it were, extinguished in mid-air, without notice or 
visible cause for its disappearance, which, as it happens 
instantaneously, and without the slightest previous diminu- 



2 Woodhouse's Astronomy, vol. i. See also Trans. Ast. Soc. vol. i. p. 325. 
See also Prof. Loomis's Introduction to Practical Astronomy, in which every 
detail of the calculation will be found illustrated by numerical examples. 



OUTLINES OF ASTRONOMY 343 

tion of its light, is always surprising; and, if the star be 
a large and bright one, even startling from its suddenness, 
The reappearance of the star, too, when the moon has 
passed over it, takes place in those cases when the bright 
side of the moon is foremost, not at the concave outline of 
the crescent, but at the invisible outline of the complete 
circle, and is scarcely less surprising, from its suddenness, 
than its disappearance in the other case. 3 

(415.) The existence of the complete circle of the disk, 
even when the moon is not full, does not, however, rest 
only on the evidence of occultations and eclipses. It may 
be seen, when the moon is crescent or waning, a few days 
before and after the new moon, with the naked eye, as a 
pale round body, to which the crescent seems attached, and 
somewhat projecting beyond its outline (which is an opti- 
cal illusion arising from the greater intensity of its light). 
The cause of this appearance will presently be explained. 
Meanwhile the fact is sufficient to show that the moon is 
not inherently luminous like the sun, but that her light 
is of an adventitious nature. And its crescent form, in- 
creasing regularly from a narrow semicircular line to a com- 



3 There is an optical illusion of a very strange and unaccountable nature 
■which has often been remarked in occultations. The star appears to advance 
actually upon and within the edge of the disk before it disappears, and that 
sometimes to a considerable depth. I have never myself witnessed this singular 
effect, but it rests on most unequivocal testimony. I have called it an optical 
illusion ; but it is barely possible that a star may shine on such occasions through 
deep fissures in the substance of the moon. The occultations of close double 
stars ought to be narrowly watched, to see whether both individuals are thus 
projected, as well as for other purposes connected with their theory. I will 
only hint at one, viz. that a double star, too close to be seen divided with any 
telescope, may yet be detected to be double by the mode of its disappearance. 
Should a considerable star, for instance, instead of undergoing instantaneous 
and complete extinction, go out by two distinct steps, following close upon each 
other; first losing a portion, then the whole remainder of its light, we may be 
sure it is a double star, though we cannot see the individuals separately. — Note 
to the edit, of 1833. 



344 



OUTLINES OF ASTRONOMY 



plete circular disk, corresponds to the appearance a globe 
would present, one hemisphere of which was black, the 
other white, when differently turned toward the eye, so as 
to present a greater or less portion of each. The obvious 
conclusion from this is, that the moon is such a globe, one- 
half of which is brightened by the rays of some luminary 
sufficiently distant to enlighten the complete hemisphere, 
and sufficiently intense to give it the degree of splendor 
we see. Now, the sun alone is competent to such an 
effect. Its distance and light suffice; and, moreover, it is 
invariably observed that, when a crescent, the bright edge 
is toward the sun, and that in proportion as the moon in 
her monthly course becomes more and more distant from 
the sun, the breadth of the crescent increases, and vice versa. 
(416.) The sun's distance being 23984 radii of the earth, 
and the moon's only 60, the former is nearly 400 times the 



€„ j£ 




latter. Lines, therefore, drawn from the sun to every part 
of the moon's orbit may be regarded as very nearly paral- 
lel. 4 Suppose, now, to be the earth, ABCD, etc., vari- 
ous positions of the moon in its orbit, and S the sun, at the 
vast distance above stated; as is shown, then, in the figure, 



4 The angle subtended by the moon's orbit, as 
mean state of things), is only 17' 12". 



seen from the sun (in the 



OUTLINES OF ASTRONOMY 345 

the hemisphere of the lunar globe turned toward it (on the 
right) will be bright, the opposite dark, wherever it may- 
stand in its orbit. Now, in the position A, when in con- 
junction with the sun, the dark part is entirely turned 
toward O, and the bright from it. In this case, then, the 
moon is not seen, it is new moon. When the moon has 
come to C, half the bright and half the dark hemisphere are 
presented to 0, and the same in the opposite situation G: 
these are the first and third quarters of the moon. Lastly, 
when at E, the whole bright face is toward the earth, the 
whole dark side from it, and it is then seen wholly bright or 
full moon. In the intermediate positions BDFH, the por- 
tions of the bright face presented to O will be at first less 
than half the visible surface, then greater, and finally less 
again, till it vanishes altogether, as it comes round again 
to A. 

(417.) These monthly changes of appearance, or phases, 
as they are called, arise, then, from the moon, an opaque 
body, being illuminated on one side by the sun, and reflect- 
ing from it, in all directions, a portion of the light so re- 
ceived. Nor let it be thought surprising that a solid sub- 
stance thus illuminated should appear to shine and again 
illuminate the earth. It is no more than a white cloud does 
standing off upon the clear blue sky. By day, the moon 
can hardly be distinguished in brightness from such a 
cloud; and, in the dusk of the evening, clouds catching 
the last rays of the sun appear with a dazzling splendor, not 
inferior to the seeming brightness of the moon at night. 6 

5 The actual illumination of the lunar surface is not much superior to that 
of weathered sandstone rock in full sunshine. I have frequently compared 
the moon setting behind the gray perpendicular facade of the Table Mountain 
illuminated by the sun just risen in the opposite quarter of the horizon, when 
it has scarcely been distinguishable in brightness from the rock in contact with 



346 OUTLINES OF ASTRONOMY 

That the earth sends also such a light to the moon, only 
probably more powerful by reason of its greater apparent 
size, 6 is agreeable to optical principles, and explains the ap- 
pearance of the dark portion of the young or waning moon 
completing its crescent (art. 413). For, when the moon is 
nearly new to the earth, the latter (so to speak) is nearly 
full to the former; it then illuminates its dark half by 
strong earth-light] and it is a portion of this, reflected back 
again, which makes it visible to us in the twilight sky. As 
the moon gains age, the earth offers it a less portion of its 
bright side, and the phenomenon in question dies away. 
The light of the full moon is estimated by Bouguer on the 
result of photometric comparisons, as only one 300000th part 
of that of the sun. 

(418.) The lunar month is determined by the recurrence 
of its phases: it reckons from new moon to new moon; that 
is, from leaving its conjunction with the sun to its return to 
conjunction. If the sun stood still, like a fixed star, the 
interval between two conjunctions would be the same as the 
period of the moon's sidereal revolution (art. 401); but, as 
the sun apparently advances in the heavens in the same 
direction with the moon, only slower, the latter has more 
than a complete sidereal period to perform to come up with 
the sun again, and will require for it a longer time, which 
is the lunar month, or, as it is generally termed in astron- 
omy, a synodical period. The difference is easily calculated 
by considering that the superfluous arc (whatever it be) is 
described by the sun with the velocity of 0° -98565 per diem, 

it. The sun and moon being nearly at equal altitudes and the atmosphere per- 
fectly free from cloud or vapor, its effect is alike on both luminaries. (H. 1848.) 
6 The apparent diameter of the moon is 32' from the earth; that of the earth 
seen from the moon is twice her horizontal parallax, or 1° 54'. The apparent 
surfaces, therefore, are as (114) 2 : (32) 2 , or as 13 : 1 nearly. 



OUTLINES OF ASTRONOMY 347 

in the same time that the moon describes that arc plus a com- 
plete revolution, with her velocity of 13 o, 17640 per diem; 
and, the times of description being identical, the spaces are 
to each other in the proportion of the velocities. Let 
Y and v be the mean angular daily motions of the sun 
and moon as above, x the superfluous arc; then Y : v : : 
360° + x : x ; and Y — v : v : : 360° : x, whence x is found ; 

x 
and - = the time in days in which the sun describes the arc 
v : 

x, that is, the synodical period = ^ = _p, if P, p are 

the periodic times of each separately, which reduced to 
numbers, gives, 29 d -530589 = 29 d 12 h 44 m 2 8 -87. 

(419.) Supposing the position of the nodes of the moon's 
orbit to permit it, when the moon stands at A (or at the new 
moon), it will intercept a part or the whole of the sun's rays, 
and cause a solar eclipse. On the other hand, when at E (or 
at the full moon), the earth O will intercept the rays of the 
sun, and cast a shadow on the moon, thereby causing a lunar 
eclipse. And this is consonant to fact, such eclipses never 
happening but at the time of the full moon. But, what is 
still more remarkable, as confirmatory of the position of the 
earth's sphericity, this shadow, which we plainly see to 
enter upon and, as it were, eat away the disk of the moon, 
is always terminated by a circular outline, though, from the 
greater size of the circle, it is only partially seen at any one 
time. Now, a body which always casts a circular shadow 
must itself be spherical. 

(420.) Eclipses of the sun are best understood by regard- 
ing the sun and moon as two independent luminaries, each 
moving according to known laws, and viewed from the 
earth; but it is also instructive to consider eclipses gen- 



848 



OUTLINES OF ASTRONOMY 



erally as arising from the shadow of one body thrown on 
another by a luminary much larger than either. Suppose, 
then, A B to represent the sun, and C D a spherical body, 
whether earth or moon, illuminated by it. If we join and 
prolong A C, B D; since A B is greater than C D, those 
lines will meet in a point E, more or less distant from the 
body C D, according to its size, and within the space CED 
(which represents a cone, since C D and A B are spheres), 
there will be a total shadow. This shadow is called the 
umbra, and a spectator situated within it can see no part of 
the sun's disk. Beyond the umbra are two diverging spaces 




(or rather, a portion of a single conical space, having K fop 
its vertex), where if a spectator be situated, as at M, he will 
see a portion only (A O 1ST P) of the sun's surface, the rest 
(B O N" P) being obscured by the earth. He will, there- 
fore, receive only partial sunshine; and the more, the nearer 
he is to the exterior borders of that cone which is called the 
penumbra. Beyond this he will see the whole sun, and be 
in full illumination. All these circumstances may be per- 
fectly well shown by holding a small globe up in the sun, 
and receiving its shadow at different distances on a sheet 
of paper. 



OUTLINES OF ASTRONOMY 349 

(421.) In a lunar eclipse (represented in the upper figure), 
the moon is seen to enter 7 the penumbra first, and by de- 
grees get involved in the umbra, the former bordering the 
latter like a smoky haze. At this period of the eclipse, and 
while yet a considerable part of the moon remains unob- 
scured, the portion involved in the umbra is invisible to the 
naked eye, though still perceptible in a telescope, and of a 
dark gray hue. But as the eclipse advances, and the en- 
lightened part diminishes in extent, and grows gradually 
more and more obscured by the advance of the penumbra, 
the eye, relieved from its glare, becomes more sensible to 
feeble impressions of light and color; and phenomena of a 
remarkable and instructive character begin to be developed. 
The umbra is seen to be very far from totally dark; and in 
its faint illumination it exhibits a gradation of color, being 
bluish, or even (by contrast) somewhat greenish, toward the 
borders for a space of about 4' or 5' of apparent angular 
breadth inward, thence passing, by delicate but rapid grada- 
tion, through rose red to a fiery or copper-colored glow, like 
that of dull red-hot iron. As the eclipse proceeds this glow 
spreads over the whole surface of the moon, which then be- 
comes on some occasions so strongly illuminated as to cast 
a very sensible shadow, and allow the spots on its surface to 
be perfectly well distinguished through a telescope. 

(422.) The cause of these singular, and sometimes very 
beautiful appearances, is the refraction of the sun's light in 
passing through our atmosphere, which at the same time 
becomes colored with the hues of sunset by the absorption 
of more or less of the violet and blue rays, as it passes 



1 The actual contact with the penumbra is never seen; the defalcation 
of light comes on so very gradually that it is not till when already deeply 
immersed, that it is perceived to be sensibly darkened. 



350 



OUTLINES OF ASTRONOMY 



through strata nearer or more remote from the earth's sur- 
face, and therefore, more or less loaded with vapor. To 
show this, let A D a be a section of the cone of the umbra, 
and FB A/of the penumbra, through their common axis 
D E S, passing through the centres E S of the earth and 
sun, and let K M h be a section of these cones at a dis- 
tance E M from E, equal to the radius of the moon's orbit, 




or 60 radii of the earth. 8 Taking this radius for unity, since 
E S, the distance of the sun, is 23984, and the semidiameter 
of the sun 111 such units, we readily calculate D E = 218, 
DM = 158, for the distances at which the apex of the geo- 
metrical umbra lies behind the earth and the moon respec- 
tively. We also find for the measure of the angle E D B, 
15' 46", and therefore D B E = 89° 44' 14', whence also we 
get M (the linear semidiameter of the umbra) = 0*725 



8 The figure is unavoidably drawn out of all proportion, and the angles 
violently exaggerated. The reader should try to draw the figure in its true 
proportions. 



OUTLINES OF ASTRONOMY 851 

(or in miles 2868), and the angle C E M, its apparent an- 
gular semidiameter as seen from E == 41' 32". And institut- 
ing similar calculations for the geometrical penumbra we get 
MK = 1-280 (5064 miles), and KEM 1° 13' 20"; and it 
may be well to remember that the doubles of these angles, 
or the mean angular diameters of the umbra and penumbra, 
are described by the moon with its mean velocity in 2 h 46 m , 
and 4 h 56 m respectively, which are therefore the respective 
durations of the total and partial obscuration of any one 
point of the moon's disk in traversing centrally the geomet- 
rical shadow. 

(423.) Were the earth devoid of atmosphere, the whole 
of the phenomena of a lunar eclipse would consist in these 
partial or total obscurations. Within the space C c the 
whole of the light, and within K C and c h a greater or less 
portion of it, would be intercepted by the solid body B b of 
the earth. The refracting atmosphere, however, extends 
from B 6, to a certain unknown, but very small distance 
B H, b A, which, acting as a convex lens, of gradually (and 
very rapidly) decreasing density, disperses all that compara- 
tively small portion of light which fa] Is upon it over a space 
bounded externally by H g, parallel and very nearly co- 
incident with B F, and internally by a line B z, the former 
representing the extreme exterior ray from the limb a of 
the sun, the latter, the extreme interior ray from the limb 
A. To avoid complication, however, we will trace only the 
courses of rays which just graze the surface at B, viz. : B z 
from the upper border, A, and B v from the lower, a, of the 
sun. Each of these rays is bent inward from its original 
course by double the amount of the horizontal refraction 
(33^) i. e. by 1° 6', because, in passing from B out of the 
atmosphere, it undergoes a deviation equal to that at enter- 



352 OUTLINES OF ASTRONOMY 

ing, and in the same direction. Instead, therefore, of pur- 
suing the courses B D, B F, these rays respectively will 
occupy the positions B z y, B v, making, with the aforesaid 
lines, the angles D B y, F B v, each 1 6'. Now we have 
found D B E = 89° 44' 14" and therefore FBE(=DBE + 
angular diam. of O) = 90° 16' 17" ; consequently the angles 
E B y and E B v will be respectively 88° 38' 14" and 89° 10' 
17", from which we conclude E z = 42-04 and E v = 6914; 
the former falling short of the moon's orbit by 17*96, and 
the latter surpassing it by 9*14 radii of the earth. 

(424.) The penumbra, therefore, of rays refracted at B, 
will be spread over the space v B y, that at H over g H c?, 
and at the intermediate points, over similar intermediate 
spaces, and through this compound of superposed penum- 
brae the moon passes during the whole of its path through 
the geometrical shadow, never attaining the absolute umbra 
B z b at all. Without going into detail as to the intensity 
of the refracted rays, it is evident that the totality of light 
so thrown into the shadow is to that which the earth inter- 
cepts, as the area of a circular section of the atmosphere to 
that of a diametrical section of the earth itself, and, there- 
fore, at all events but feeble. And it is still further en- 
feebled by actual clouds suspended in that portion of the 
air which forms the visible border of the earth's disk as 
seen from the moon, as well as by the general want of 
transparency caused by invisible vapor, which is especially 
effective in the lowermost strata, within three or four miles 
of the surface, and which will impart to all the rays they 
transmit the ruddy hue of sunset, only of double the depth 
of tint which we admire in our glowing sunsets, by reason 
of the rays having to traverse twice as great a thickness of 
atmosphere. This redness will be most intense at the 



OUTLINES OF ASTRONOMY 353 

points #, y 1 of the moon's path through the umbra, and 
will thence degrade very rapidly outwardly, over the spaces 
x C, yc, less so inwardly, over x y. And at C, c, its hue 
will be mingled with the bluish or greenish light which 
the atmosphere scatters by irregular dispersion, or in other 
words by our twilight (art. 44). Nor will the phenomenon 
be uniformly conspicuous at all times. Supposing a gener- 
ally and deeply clouded state of the atmosphere around the 
edge of the earth's disk visible from the moon (i.e. around 
that great circle of the earth, in which, at the moment the 
sun is in the horizon) little or no refracted light may reach 
the moon. 9 Supposing that circle partly clouded and partly 
clear, patches of red light corresponding to the clear por- 
tions will be thrown into the umbra, and may give rise to 
various and changeable distributions of light on the eclipsed 
disk; 10 while, if entirely clear, the eclipse will be remark- 
able for the conspicuousness of the moon during the whole 
or a part of its immersion in the umbra. 11 

(425.) Owing to the great size of the earth, the cone of 
its umbra always projects far beyond the moon; so that, 
if, at the time of a lunar eclipse, the moon's path be prop- 
erly directed, it is sure to pass through the umbra. This 
is not, however, the case in solar eclipses. It so happens, 
from the adjustment of the size and distance of the moon, 
that the extremity of her umbra always falls near the earth, 
but sometimes attains and sometimes falls short of its sur- 
face. In the former case (represented in the lower figure, 

9 As in the eclipses of June 5, 1620, April 25, 1642. Lalande, Ast. 1769. 
Also December 9, 1601, and June 10, 1816, on which occasion the moon was 
totally invisible even in telescopes. 

10 As in the eclipse of Oct. 13, 1837, observed by the author. 

11 As in that of March 19, 1848, when the moon is described as giving 
"good light" during more than an hour after its total immersion, and some 
persons even doubted its being eclipsed. (Notices of R. Ast. Soc. viii. p. 132.) 



354 OUTLINES OF ASTRONOMY 

art. 420) a black spot, surrounded by a fainter shadow, is 
formed, beyond which there is no eclipse on any part of the 
earth, but within which there may be either a total or partial 
one, as the spectator is within the umbra or penumbra. 
When the apex of the umbra falls on the surface, the moon 
at that point will appear, for an instant, to just cover the 
sun; but, when it falls short, there will be no total eclipse 
on any part of the earth; but a spectator, situated in or near 
the prolongation of the axis of the cone, will see the whole 
of the moon on the sun, although not large enough to cover 
it, i.e. he will witness an annular eclipse, a phenomenon to 
which much interest is attached by reason of some curious 
optical phenomena first observed by Mr. Baily at the mo- 
ments of the forming and breaking of the annulus, like 
beads of light alternating with black thready elongations 
of the moon's limb, known by the name of "Baily's beads." 
(426.) Owing to a remarkable enough adjustment of the 
periods in which the moon's sy nodical revolution, and that 
of her nodes, are performed; eclipses return after a certain 
period, very nearly in the same order and of the same mag- 
nitude. For 223 of the moon's mean synodical revolutions, 
or lunations, as they are called, will be found to occupy 
6585*32 days, and nineteen complete synodical revolutions 
of the node to occupy 6585*78. The difference in the mean 
position of the node, then, at the beginning and end of 223 
lunations, is nearly insensible; so that a recurrence of all 
eclipses within that interval must take place. Accordingly, 
this period of 223 lunations, or eighteen years and ten days, 
is a very important one in the calculation of eclipses. It is 
supposed to have been known to the Chaldeans, the earliest 
astronomers, the regular return of eclipses having been 
known as a physical fact for ages before their exact theory 



OUTLINES OF ASTRONOMY 355 

was understood. In this period there occur ordinarily 70 
eclipses, 29 of the moon, and 41 of the sun, visible in some 
part of the earth. Seven eclipses of either sun or moon at 
most, and two at least (both of the sun), may occur in a 
year. 

(427.) The commencement, duration, and magnitude of 
a lunar eclipse are much more easily calculated than those 
of a solar, being independent of the position of the spectator 
on the earth's surface, and the same as if viewed from its 
centre. The common centre of the umbra and penumbra 
lies always in the ecliptic, at a point opposite to the sun, 
and the path described by the moon in passing through it 
is its true orbit as it stands at the moment of the full moon. 
In this orbit, its position, at every instant, is known from 
the lunar tables and ephemeris; and all we have, therefore, 
to ascertain, is, the moment when the distance between the 
moon's centre and the centre of the shadow is exactly equal 
to the sum of the semidiameters of the moon and penumbra, 
or of the moon and umbra, to know when it enters upon 
and leaves them respectively. No lunar eclipse can take 
place, if, at the moment of the full moon, the sun be at a 
greater angular distance from the. node of the moon's orbit 
than 11° 21', meaning by an eclipse the immersion of any 
part of the moon in the umbra, as its contact with the 
penumbra cannot be observed (see note to art. 421). 

(428.) The dimensions of the shadow, at the place where 
it crosses the moon's path, require us to know the distances 
of the sun and moon at the time. These are variable ; but 
are calculated and set down, as well as their semidiameters, 
for every day, in the ephemeris, so that none of the data are 
wanting. The sun's distance is easily calculated from its 
elliptic orbit; but the moon's is a matter of more difficulty, 



356 OUTLINES OF ASTRONOMY 

by reason of the progressive motion of the axis of the lunar 
orbit. (Art. 409.) Both, however, are readily obtained 
from the ephemeris for every day; the sun's distance being 
given explicitly and the moon's implicitly, from her tabu- 
lated apparent diameter. 

(428 a.) It deserves to be mentioned that the moon may 
be seen eclipsed while the sun is yet above the horizon by 
a spectator properly situated, so that both luminaries being 
on his mathematical horizon shall be raised above it by 
refraction, which (art. 43) exceeds the apparent diameter of 
either. This singular conjuncture of circumstances is said 
to have been observed from Montmartre, near Paris, by 
the assembled academicians of that city in A.D. 1668. 

(428 b.) The full moon which happens on or nearest to 
the 21st of September is called the harvest moon, because 
it rises from night to night, after the full, more nearly after 
sunset than any other full moon in the year, and is therefore 
favorable for evening work in carrying in the late crops. 
Suppose the full moon to happen on that day (the time of 
the autumnal equinox) the sun is then entering Libra, and 
the moon Aries, the former setting due west, the latter 
rising due east ; the southern half of the ecliptic is then 
entirely above and the northern below the horizon, and the 
ecliptic itself makes then the least possible angle with 
the horizon. In advancing then 12°, or one day's motion, 
along the ecliptic (or along its own orbit, which is not 
much inclined to it) it will become less depressed below 
the horizon, and have, therefore, a less hour angle to travel 
over by the diurnal motion after sunset the next night to 
bring it into view than at any other time. The most favor- 
able harvest moon is when the full moon, falling on the 
21st of September, happens at the same time to be in 



OUTLINES OF ASTRONOMY 357 

the ascending node of her orbit, which then coincides 
with the vernal equinox. 

(429.) The physical constitution of the moon is better 
known to us than that of any other heavenly body. By 
the aid of telescopes, we discern inequalities in its surface 
which can be no other than mountains and valleys — for this 
plain reason, that we see the shadows cast by the former in 
the exact proportion as to length which they ought to have, 
when we take into account the inclination of the sun's rays 
to that part of the moon's surface on which they stand. 
The convex outline of the limb turned toward the sun is 
always circular, and very nearly smooth; but the opposite 
border of the enlightened part, which (were the moon a 
perfect sphere) ought to be an exact and sharply denned 
ellipse, is always observed to be extremely ragged, and 
indented with deep recesses and prominent points. The 
mountains near this edge cast long black shadows, as they 
should evidently do, when we consider that the sun is in 
the act of rising or setting to the parts of the moon so 
circumstanced. But as the enlightened edge advances 
beyond them, i.e. as the sun to them gains altitude, their 
shadows shorten; and at the full moon, when all the light 
falls in our line of sight, no shadows are seen on any part 
of her surface. From micrometrieal measures of the lengths 
of the shadows of the more conspicuous mountains, taken 
under the most favorable circumstances, the heights of many 
of them have been calculated. Messrs. Beer and Maedler, 
in their elaborate work, entitled "Der Mond," have given 
a list of heights resulting from such measurements, for no 
less than 1095 lunar mountains, among which occur all 
degrees of elevation up to 3569 toises (22,823 British feet), 
or about 1400 feet higher than Chimborazo in the Andes. 



S58 OUTLINES OF ASTRONOMY 

The existence of such mountains is further corroborated 
bj their appearance, as small points or islands of light 
beyond the extreme edge of the enlightened part, which 
are their tops catching the sunbeams before the inter- 
mediate plain, and which, as the light advances, at length 
connect themselves with it, and appear as prominences 
from the general edge. 

(430.) The generality of the lunar mountains present 
a striking uniformity and singularity of aspect. They are 
wonderfully numerous, especially toward the southern por- 
tion of the disk, occupying by far the larger portion of the 
surface, and almost universally of an exactly circular or 
cup-shaped form, foreshortened, however, into ellipses to- 
ward the limb; but the larger have for the most part flat 
bottoms within, from which rises centrally a small, steep, 
conical hill. They offer, in short, in its highest perfec- 
tion, the true volcanic character, as it may be seen in the 
crater of Vesuvius, and in a map of the volcanic districts 
of the Campi Phlegrsei 19 or the Puy de Dome, but with this 
remarkable peculiarity; viz. that the bottoms of many of 
the craters are very deeply depressed below the general 
surface of the moon, the internal depth being often twice 
or three times the external height. In some of the prin- 
cipal ones, decisive marks of volcanic stratification, arising 
from successive deposits of ejected matter, and evident 
indications of lava currents streaming outward in all di- 
rections, may be clearly traced with powerful telescopes. 
(See Plate Y.fig. 2.) 13 In Lord Kosse's magnificent reflec- 
tor, the flat bottom of the crater called Albategnius is seen 
to be strewed with blocks not visible in inferior telescopes, 

11 See Breislak's map of the environs of Naples, and Desmarest's of Auvergna 
18 From a drawing taken with a reflector of twenty feet focal length (h). 



OUTLINES OF ASTRONOMY 359 

while the exterior of another (Aristillus) is all hatched over 
with deep gullies radiating toward its centre. What is, 
moreover, extremely singular in the geology of the moon 
is, that, although nothing having the character of seas can 
be traced (for the dusky spots, which are commonly called 
seas, when closely examined, present appearances incompat- 
ible with the supposition of deep water), yet there are large 
regions perfectly level, and apparently of a decided alluvial 
character; as there are also here and there chains of moun- 
tains whose appearance suggests no suspicion of volcanic 
origin. [See 430 a, in Note H.] 

(431.) We perceive on the moon no clouds, nor any 
other decisive indications of an atmosphere. Were there 
any, it could not fail to be perceived in the occultations 
of stars and the phenomena of solar eclipses, as well as 
in a great variety of other phenomena. The moon's di- 
ameter, for example, as measured micrometrically, and as 
estimated by the interval between the disappearance and re- 
appearance of a star in an occultation, ought to differ by 
twice the horizontal refraction at the moon's surface. No 
appreciable difference being perceived, we are entitled to 
conclude the non-existence of any atmosphere at its edge 
dense enough to cause a refraction of 1", i. e. having one 
1980th part of the density of the earth's atmosphere. In 
a solar eclipse, the existence of any sensible refracting at- 
mosphere in the moon would enable us to trace the limb 
of the latter beyond the cusps, externally to the sun's disk, 
by a narrow, but brilliant line of light, extending to some 
distance along its edge. No such phenomenon is seen. 
Very faint stars ought to be extinguished before occulta- 
tion, were any appreciable amount of vapor suspended near 
the surf ace of the moon. But such is not the case: when 



360 OUTLINES OF ASTRONOMY 

occulted at the bright edge, indeed, the light of the moon 
extinguishes small stars, and even at the dark limb, the 
glare in the sky caused by the near presence of the moon 
renders the occultation of very minute stars unobservable. 
But during the continuance of a total lunar eclipse, stars 
of the tenth and eleventh magnitude are seen to come up 
to the limb, and undergo sudden extinction as well as those 
of greater brightness. 14 Hence, the climate of the moon 
must be very extraordinary; the alternation being that of 
unmitigated and burning sunshine fiercer than an equato- 
rial noon, continued for a whole fortnight, and the keenest 
severity of frost, far exceeding that of our polar winters, 
for an equal time. Such a disposition of things must pro- 
duce a constant transfer of whatever moisture may exist on 
its surface, from the point beneath the sun to that opposite, 
by distillation in vacuo after the manner of the little instru- 
ment called a cryophorus. The consequence must be abso- 
lute aridity below the vertical sun, constant accretion of 
hoarfrost in the opposite region, and, perhaps, a narrow 
zone of running water at the borders of the enlightened 
hemisphere." It is possible, then, that evaporation on the 
one hand, and condensation on the other, may to a certain 
extent preserve an equilibrium of temperature, and mitigate 
the extreme severity of both climates; but this process, 
which would imply the continual generation and destruc- 
tion of an atmosphere of aqueous vapor, must, in conform- 
ity with what has been said above of a lunar atmosphere, 
be confined within very narrow limits. - 

(432.) Though the surface of the full moon exposed 
to us must necessarily be very much heated — possibly to a 
degree much exceeding that of boiling water — yet we feel 

14 As observed by myself in eclipse of Oct. 13, 1837. 16 So in ed. of 1833. 



OUTLINES OF ASTRONOMY 361 

no heat from it, and even in the focus of large reflectors 
it fails to affect the thermometer. No doubt, therefore, its 
heat (conformably to what is observed of that of bodies 
heated below the point of luminosity) is much more readily 
absorbed in traversing transparent media than direct solar 
heat, and is extinguished in the upper regions of our atmos- 
phere, never reaching the surface of the earth at all. Some 
probability is given to this by the tendency to disappearance 
of clouds under the full moon, a meteorological fact (for as 
such we think it fully entitled to rank 16 ) for which it is 
necessary to seek a cause, and for which no other rational 
explanation seems to offer. As for any other influence of 
the moon on the weather, we have no decisive evidence 
in its favor. 

(433.) A circle of one second in diameter, as seen from 
the earth, on the surface of the moon, contains about a 
square mile. Telescopes, therefore, must yet be greatly 
improved, before we could expect to see signs of inhabi- 
tants, as manifested by edifices or by changes on the sur- 
face of the soil. It should, however, be observed, that, 
owing to the small density of the materials of the moon, 
and the comparatively feeble gravitation of bodies on her 
surface, muscular force would there go six times as far in 
overcoming the weight of materials as on the earth. Owing 
to the want of air, however, it seems impossible that any 
form of life, analogous to those on earth, can subsist there. 

16 From my own observations, made quite independently of any knowledge 
of such a tendency having been observed by others. Humboldt, however, in 
his Personal Narrative, speaks of it as well known to the pilots and seamen 
of Spanish America. 

M. Arago has shown from a comparison of rain, registered as having fallen 
during a long period, that a slight preponderance in respect of quantity falls 
near the new moon over that which falls near the full. This would be a natural 
and necessary consequence of a preponderance of a cloudless sky about the full, 
and forms, therefore, part and parcel of the same meteorological fact 
Astronomy— Vol. XIX— 16. 



362 OUTLINES OF ASTRONOMY 

No appearance indicating vegetation, or the slightest varia- 
tion of surface, which can, in our opinion, fairly be ascribed 
to change of season, can anywhere be discerned. 

(434.) The lunar summer and winter arise, in fact, from 
the rotation of the moon on its own axis, the period of 
which rotation is exactly equal to its sidereal revolution 
about the earth, and is performed in a plane 1° 30' 11" 
inclined to the ecliptic, whose ascending node is always 
precisely coincident with the descending node of the lunar 
orbit. So that the axis of rotation describes a conical sur- 
face about the pole of the ecliptic in one revolution of the 
node. The remarkable coincidence of the two rotations, 
that about the axis and that about the earth, which at 
first sight would seem perfectly distinct, has been asserted 
(but we think somewhat too hastily 17 ) to be a consequence 
of the general laws to be explained hereafter. Be that how 
it may, it is the cause why we always see the same face of 
the moon, and have no knowledge of the other side. 18 

(435.) The moon's rotation on her axis is uniform; but 
since her motion in her orbit (like that of the sun) is not 
so, we are enabled to look a few degrees round the equa- 
torial parts of her visible border, on the eastern or western 
side, according to circumstances; or, in other words, the 
line joining the centres of the earth and moon fluctuates a 
little in its position, from its mean or average intersection 

17 See "Edinburgh Review," No. 1*75, p. 192. 

18 Strange to say, there are persons who find it difficult to regard as a rota- 
tion on its own axis, that peculiarity of the moon's motion which consists in 
its keeping the same face always toward the earth. Should any of our readers 
be in this predicament, we recommend him to plant a staff upright in the 
ground, and, grasping it with both hands, walk round it, keeping as close to 
it as possible, with his face always turned toward it ; when the unmistakable 
sensation of giddiness will effectually satisfy him of the fact of his rotation on 
his own axis, or he may walk round a tree, always facing it, and carrying a 
compass in his hand, and while watching the needle during a few circuits 
endeavor to persuade himself that he does not turn upon his own centre. 



OUTLINES OF ASTRONOMY 363 

with her surface, to the east or westward. And, moreover, 
since the axis about which she revolves is neither exactly 
perpendicular to her orbit, nor holds an invariable direction 
in space, her poles come alternately into view for a small 
space at the edges of her disk. These phenomena are 
known by the name of librations. In consequence of these 
two distinct kinds of libration, the same identical point of 
the moon's surface is not always the centre of her disk, and 
we therefore get sight of a zone of a few degrees in breadth 
on all sides of the border, beyond an exact hemisphere. 

(436.) If there be inhabitants in the side of the moon 
turned toward us, the earth must present to them the ex- 
traordinary appearance of a moon of nearly 2° in diameter, 
exhibiting phases complementary to those which we see the 
moon to do, but immovably fixed in their shy (or, at least, 
changing its apparent place only by the small amount of the 
libration), while the stars must seem to pass slowly beside 
and behind it. It will appear clouded with variable spots, 
and belted with equatorial and tropical zones correspond- 
ing to our trade-winds; and it may be doubted whether, in 
their perpetual change, the outlines of our continents and 
seas can ever be clearly discerned. During a solar eclipse, 
the earth's atmosphere will become visible as a narrow, but 
bright, luminous ring of a ruddy color, where it rests on 
the earth, gradually passing into faint blue, encircling the 
whole or part of the dark disk of the earth, the remainder 
being dark and ragged with clouds. 

(436 a.) On the subject of the moon's habitability, the 
complete absence of air noticed in art. 431, if general over 
her whole surface, would of course be decisive. Some con- 
siderations of a contrary nature, however, suggest them- 
selves in consequence of a remark lately made by Prof. 



364 OUTLINES OF ASTRONOMY 

Hansen, viz. that the fact of the moon turning always the 
same face toward the earth is in all probability the result 
of an elongation of its figure in the direction of a line join- 
ing the centres of both the bodies acting conjointly with a 
non- coincidence of its centre of gravity with its centre of sym- 
metry. To the middle of the length of a stick, loaded with 
a heavy weight at one end and a light one at the other, at- 
tach a string, and swing it round. The heavy weight will 
assume and maintain a position in the circulation of the 
joint mass further from the hand than the lighter. This is 
not improbably what takes place in the moon. Anticipat- 
ing to a certain extent what he will find more fully detailed 
in the next chapter, the reader may consider the moon as 
retained in her orbit about the earth by some coercing 
power analogous to that which the hand exerts on the 
compound mass above described through the string. Sup- 
pose, then, its globe made up of materials not homoge- 
neous, and so disposed in its interior that some consid- 
erable preponderance of weight should exist excentrically 
situated: then it will be easily apprehended that the por- 
tion of its surface nearer to that heavier portion of its solid 
content, under all the circumstances of a rotation so ad- 
justed, will permanently occupy the situation most remote 
from the earth. Let us now consider what may be expected 
to be the distribution of air, water, or other fluid on the 
surface of such a globe, supposing its quantity not sufficient 
to cover and drown the whole mass. It will run toward the 
lowest place, that is to say, not the nearest to the centre of 
figure or to the central point of the mere space occupied by 
the moon, but to the centre of the mass, or what is called 
in mechanics the centre of gravity. There will be formed 
there an ocean, of more or less extent according to the 



OUTLINES OF ASTRONOMY 365 

quantity of fluid, directly over the heavier nucleus, while 
the lighter portion of the solid material will stand out as a 
continent on the opposite side. And the height above the 
level of such ocean to which it will project will be greater, 
the greater the excentricity of the centre of gravity. Sup- 
pose then that in the case of the moon this excentricity 
should amount to some thirty or forty miles, such would 
be the general elevation of the lunar land (or the portion 
turned earthward) above its ocean, so that the whole of that 
portion of the moon we see would in fact come to be 
regarded as a mountainous elevation above the sea level. 
(436 b.) In what regards its assumption of a definite 
level, air obeys precisely the same hydrostatical laws as 
water. The lunar atmosphere would rest upon the lunar 
ocean, and form in its basin a lake of air, whose upper 
portions at an altitude such as we are now contemplating 
would be of excessive tenuity, especially should the lunar 
provision of air be less abundant in proportion than our 
own. It by no means follows, then, from the absence of 
visible indications of water or air on this side of the moon, 
that the other is equally destitute of them, and equally 
unfitted for maintaining animal or vegetable life. Some 
slight approach to such a state of things actually obtains 
on the earth itself. Nearly all the land is collected in one 
of its hemispheres, and much the larger portion of the sea 
in the opposite (art. 284). There is evidently an excess of 
heavy material vertically beneath the middle of the Pacific ; 
while not very remote from the point of the globe diametri- 
cally opposite rises the great tableland of India, and the 
Himalaya chain, on the summits of which the air has not 
more than a third of the density it has on the sea level, and 
from which animated existence is forever excluded. 



366 OUTLINES OF ASTRONOMY 

(437.) The best charts of the lunar surface are those of 
Cassini, of Eussel (engraved from drawings, made by the 
aid of a seven feet reflecting telescope), the seleno- topo- 
graphical charts of Lohrmann, and the very elaborate 
projection of Beer and Maedler accompanying their work 
already cited. Madame Witte, a Hanoverian lady, has re- 
cently succeeded in producing from her own observations, 
aided by Maedler's charts, more than one complete model of 
the whole visible lunar hemisphere, of the most perfect 
kind, the result of incredible diligence and assiduity. 
Single craters have also been modelled on a large scale, 
both by her and Mr. Nasmyth. Still more recently (1851- 
1863), photography has been applied with success to the 
exact delineation of the lunar surface, by Mr. Whipple, 
using for this purpose the great Fraunhofer equatorial of 
the Observatory at Cambridge, U.S.; by Mr. Hartnup, with 
the equatorial of the Liverpool Observatory; but more es- 
pecially by Mr. De la Eue, with an equatorially mounted 
Newtonian reflector of 13 inches aperture and 10 feet focal 
length. [See § 437 a, in Note I.] 



CHAPTEK VIII 

Of Terrestrial Gravity — Of the Law of Universal Gravitation — Paths of Pro- 
jectiles ; Apparent, Real — The Moon Retained in her Orbit by Gravity 
— Its Law of Diminution — Laws of Elliptic Motion — Orbit of the Earth 
Round the Sun in Accordance with these Laws — Masses of the Earth 
and Sun Compared— Density of the Sun — Force of Gravity at its Sur- 
face — Disturbing Effect of the Sun on the Moon's Motion 

(438.) The reader has now been made acquainted with 
the chief phenomena of the motions of the earth in its orbit 
round the sun, and of the moon about the earth. — We come 
next to speak of the physical cause which maintains and 



OUTLINES OF ASTRONOMY 367 

perpetuates these motions, and causes the massive bodies so 
revolving to deviate continually from the directions they 
would naturally seek to follow, in pursuance of the first 
law of motion, ' and bend their courses into curves concave 
to their centres. 

(439.) Whatever attempts may have been made by meta- 
physical writers to reason away the connection of cause and 
effect, and fritter it down into the unsatisfactory relation of 
habitual sequence, 2 it is certain that the conception of some 
more real and intimate connection is quite as strongly im- 
pressed upon the human mind as that of the existence of 
an external world — the vindication of whose reality has 
(strange to say) been regarded as an achievement of no 
common merit in the annals of this branch of philosophy. 
It is our own immediate consciousness of effort, when we 
exert force to put matter in motion, or to oppose and 
neutralize force, which gives us this internal conviction 
of power and causation so far as it refers to the material 
world, and compels us to believe that whenever we see 
material objects put in motion from a state of rest, or de- 
flected from their rectilinear paths and changed in their 
velocities if already in motion, it is in consequence of such 
an effort somehow exerted, though not accompanied with 
our consciousness. That such an effort should be exerted 
with success through an interposed space, is no doubt difn- 



1 Princip. Lex. I. 

2 See Brown "On Cause and Effect" — a work of great acuteness and subtlety 
of reasoning on some points, but in which, the whole train of argument is vitiated 
by one enormous oversight; the omission, namely, of a distinct and immediate 
personal consciousness of causation in his enumeration of that sequence of events, 
by which the volition of the mind is made to terminate in the motion of material 
objects. I mean the consciousness of effort, accompanied with intention thereby 
to accomplish an end, as a thing entirely distinct from mere desire or volition on 
the one hand, and from mere spasmodic contraction of muscles on the other. 
Brown, 3d edit. Edin. 1818, p. 47. (Note to edition of 1833.) 



368 OUTLINES OF ASTRONOMY 

cult to conceive. But the difficulty is no way alleviated by 
the interposition of any kind of material communication. 
The action of mind on matter admits of no explanation in 
words or elucidation by parallels. We know it is a fact, 
but afre utterly incapable of analyzing it as a process. 

(440.) All bodies with which we are acquainted, when 
raised into the air and quietly abandoned, descend to the 
earth's surface in lines perpendicular to it. They are there- 
fore urged thereto by a force or effort, which it is but 
reasonable to regard as the direct or indirect result of a 
consciousness and a will existing somewhere, though beyond 
our power to trace, which force we term gravity, and whose 
tendency or direction, as universal experience teaches, is 
toward the earth's centre; or rather, to speak strictly, with 
reference to its spheroidal figure, perpendicular to the sur- 
face of still water. But if we cast a body obliquely into the 
air, this* tendency, though not extinguished or diminished, 
is materially modified in its ultimate effect. The upward 
impetus we give the stone is, it is true, after a time de- 
stroyed, and a downward one communicated to it, which 
ultimately brings it to the surface, where it is opposed in 
its further progress, and brought to rest. But all the while 
it has been continually deflected or bent aside from its rec- 
tilinear progress, and made to describe a curved line con- 
cave to the earth's centre; and having a highest point, vertex, 
or apogee, just as the moon has in its orbit, where the direc- 
tion of its motion is perpendicular to the radius. 

(441.) When the stone which we fling obliquely upward 
meets and is stopped in its descent by the earth's surface, 
its motion is not toward the centre, but inclined to the 
earth's radius at the same angle as when it quitted our 
hand. As we are sure that, if not stopped by the resist- 



OUTLINES OF ASTRONOMY 369 

ance of the earth, it would continue to descend, and that 
obliquely, what presumption, we may ask, is there that it 
would ever reach the centre toward which its motion, in 
no part of its visible course, was ever directed ? What 
reason have we to believe that it might not rather circulate 
round it, as the moon does round the earth, returning again 
to the point it set out from, after completing an elliptic 
orbit of which the earth's centre occupies the lower focus? 
And if so, is it not reasonable to imagine that the same 
force of gravity may (since we know that it is exerted at 
all accessible heights above the surface, and even in the 
highest regions of the atmosphere) extend as far as 60 radii 
of the earth, or to the moon ? and may not this be the 
power — for some power there must be — which deflects her 
at every instant from the tangent of her orbit, and keeps 
her in the elliptic path which experience teaches us she 
actually pursues ? 

(442.) If a stone be whirled round at the end of a string 
it will stretch the string by a centrifugal force, which, if the 
speed of rotation be sufficiently increased, will at length 
break the string, and let the stone escape. However strong 
the string, it may, by a sufficient rotary velocity of the 
stone, be brought to the utmost tension it will bear without 
breaking; and if we know what weight it is capable of 
carrying, the velocity necessary for this purpose is easily 
calculated. Suppose, now, a string to connect the earth's 
centre with a weight at its surface, whose strength should 
be just sufficient to sustain that weight suspended from it 
Let us, however, for a moment imagine gravity to have no 
existence, and that the weight is made to revolve with the 
limiting velocity which that string can barely counteract, 
then will its tension be just equal to the weight of the 



370 OUTLINES OF ASTRONOMY 

revolving body; and any power which should continually 
urge the body toward the centre with a force equal to its 
weight would perform the office, and might supply the 
place of the string, if divided. Divide it then, and in its 
place let gravity act, and the body will circulate as before; 
its tendency to the centre, or its weight, being just balanced 
by its centrifugal force. Knowing the radius of the earth, 
we can calculate by the principles of mechanics the peri- 
odical time in which a body so balanced must circulate to 
keep it up; and this appears to be l h 23 m 22 8 c 

(443.) If we make the same calculation for a body at the 
distance of the moon, supposing its weight or gravity the same 
as at the earth 1 s surface, we shall find the period required to 
be 10 h 45 m 30 s . The actual period of the moon's revolution, 
however, is 27 d 7 h 43 m ; and hence it is clear that the moon's 
velocity is not nearly sufficient to sustain it against such 
a power, supposing it to revolve in a circle, or neglecting 
(for the present) the slight ellipticity of its orbit. In order 
that a body at the distance of the moon (or the moon itself) 
should be capable of keeping its distance from the earth by 
the outward effort of its centrifugal force, while yet its time 
of revolution should be what the moon's actually is, it will 
appear 3 that gravity, instead of being as intense as at the 
surface, would require to be very nearly 3600 times less 
energetic; or, in other words, that its intensity is so en- 
feebled by the remoteness of the body on which it acts, 
as to be capable of producing in it, in the same time, only 
3-gL-^th part of the motion which it would impart to the same 
mass of matter at the earth's surface. 

(444.) The distance of the moon from the earth's centre 
is very nearly sixty times the distance from the centre to 

3 Newton, Frincip. b. i., Prop. 4, Cor. 2. 



OUTLINES OF ASTRONOMY 371 

the surface, and 3600 : 1 :: 60 a : P; so that the proportion 
in which we must admit the earth's gravity to be enfeebled 
at the moon's distance, if it be really the force which retains 
the moon in her orbit, must be (at least in this particular 
instance) that of the squares of the distances at which it is 
compared. Now, in such a diminution of energy with in- 
crease of distance, there is nothing prima facie inadmissible. 
Emanations from a centre, such as light and heat, do really 
diminish in intensity by increase of distance, and in this 
identical proportion; and though we cannot certainly argue 
much from this analogy, yet we do see that the power of 
magnetic and electric attractions and repulsions is actually 
enfeebled by distance, and much more rapidly than in the 
simple proportion of the increased distances. The argu- 
ment, therefore, stands thus : — On the one hand, Gravity is 
a real power, of whose agency we have daily experience. 
We know that it extends to the greatest accessible heights, 
and far beyond; and we see no reason for drawing a line at 
any particular height, and there asserting that it must cease 
entirely; though we have analogies to lead us to suppose 
its energy may diminish as we ascend to great heights from 
the surface, such as that of the moon. On the other hand 
we are sure the moon is urged toward the earth by some 
power which retains her in her orbit and that the intensity 
of this power is such as would correspond to a gravity 
diminished in the proportion — otherwise not improbable — 
of the squares of the distances. If gravity be not that 
power, there must exist some other; and, besides this, 
gravity must cease at some inferior level, or the nature of 
the moon must be different from that of ponderable matter; 
— for if not, it would be urged by both powers, and therefore 
too much urged and forced inward from her path. 



372 OUTLINES OF ASTRONOMY 

(445.) It is on such an argument that Newton is under- 
stood to have rested, in the first instance, and provisionally, 
his law of universal gravitation, which may be thus ab- 
stractly stated: — "Every particle of matter in the universe 
attracts every other particle, with a force directly propor- 
tioned to the mass of the attracting particle, and inversely 
to the square of the distance between them/' In this ab- 
stract and general form, however, the proposition is not 
applicable to the case before us. The earth and moon are 
not mere particles, but great spherical bodies, and to such 
the general law does not immediately apply; and, before 
we can make it applicable, it becomes necessary to inquire 
what will be the force with which a congeries of particles, 
constituting a solid mass of any assigned figure, will attract 
another such collection of material atoms. This problem 
is one purely dynamical, and, in this its general form, is 
of extreme difficulty. Fortunately, however, for human 
knowledge when the attracting and attracted bodies are 
spheres, it admits of an easy and direct solution. Newton 
himself has shown (Princip. b. i. prop. 75) that, in that case, 
the attraction is precisely the same as if the whole matter of 
each sphere were collected into its centre, and the spheres 
were single particles there placed ; so that, in this case, the 
general law applies in its strict wording. The effect of 
the trifling deviation of the earth from a spherical form 
is of too minute an order to need attention at present. It 
is, however, perceptible, and may be hereafter noticed. 

(446.) The next step in the Newtonian argument is one 
which divests the law of gravitation of its provisional 
character, as derived from a loose and superficial considera- 
tion of the lunar orbit as a circle described with an average 
or mean velocity, and elevates it to the rank of a general 



OUTLINES OF ASTRONOMY 373 

and primordial relation by proving its applicability to the 
state of existing nature in all its circumstances. This step 
consists in demonstrating, as he has done 4 {Princip. i. 17, i. 
75), that, under the influence of such an attractive force 
mutually urging two spherical gravitating bodies toward 
each other, they will each, when moving in each other's 
neighborhood, be deflected into an orbit concave toward 
the other, and describe, one about the other regarded as 
fixed, or both round their common centre of gravity, curves 
whose forms are limited to those figures known in geometry 
by the general name of conic sections. It will depend, he 
shows, in any assigned case, upon the particular circum- 
stances of velocity, distance, and direction, which of these 
curves shall be described — whether an ellipse, a circle, a 
parabola, or a hyperbola; but one or other it must be; and 
any one of any degree of excentricity it may be, according 
to the circumstances of the case; and, in all cases, the point 
to which the motion is referred, whether it be the centre of 
one of the spheres, or their common centre of gravity, will 
of necessity be the focus of the conic section described. He 
shows, furthermore {Princip. i. 1.), that, in every case, the 
angular velocity with which the line joining their centres 
moves, must be inversely proportional to the square of their 
mutual distance, and that equal areas of the curves described 
will be swept over by their line of junction in equal times. 

4 We refer for these fundamental propositions, as a point of duty, to the 
immortal work in which they were first propounded. It is impossible for us, in 
this volume, to go into these investigations : even did our limits permit, it would 
be utterly inconsistent with our plan; a general idea, however, of their conduct 
will be given in the next chapter. We trust that the careful and attentive study 
of the Principia in its original form will never be laid aside, whatever be the 
improvements of the modern analysis as respects facility of calculation and ex- 
pression. From no other quarter can a thorough -and complete comprehension 
of the mechanism of our system (so far as the immediate scope of that work 
extends), be anything like so well, and we may add, so easily obtained. 



374 OUTLINES OF ASTRONOMY 

(447.) All this is in conformity with what we have stated 
of the solar and lunar movements. Their orbits are ellipses, 
but of different degrees of excentricity ; and this circum- 
stance already indicates the general applicability of the 
principles in question. 

(448.) But here we have already, by a natural and ready 
implication (such is always the progress of generalization), 
taken a further and most important step, almost unperceived. 
We have extended the action of gravity to the case of the 
earth and sun, to a distance immensely greater than that 
of the moon, and to a body apparently quite of a different 
nature than either. Are we justified in this? or, at all 
events, are there no modifications introduced by the change 
of data, if not into the general expression, at least into the 
particular interpretation, of the law of gravitation? Now, 
the moment we come to numbers, an obvious incongruity 
strikes us. "When we calculate, as above, from the known 
distance of the sun (art. 357), and from the period in which 
the earth circulates about it (art. 305), what must be the 
centrifugal force of the latter by which the sun's attraction 
is balanced (and which, therefore, becomes an exact meas- 
ure of the sun's attractive energy as exerted on the earth), 
we find it to be immensely greater than would suffice to 
counteract the earth's attraction on an equal body at that 
distance — greater in the high proportion of 354936 to 1. It 
is clear, then, that if the earth be retained in its orbit about 
the sun by solar attraction, conformable in its rate of diminu- 
tion with the general law, this force must be no less than 
354936 times more intense than what the earth would be 
capable of exerting, cceteris paribus, at an equal distance. 

(449.) What, then, are we to understand from this result? 
Simply this — that the sun attracts as a collection of 354936 



OUTLINES OF ASTRONOMY 375 

earths occupying its place would do, or, in other words, 
that the sun contains 354936 times the mass or quantity of 
ponderable matter that the earth consists of. Nor let this 
conclusion startle us. We have only to recall what has 
been already shown in art. 358 of the gigantic dimensions 
of this magnificent body, to perceive that, in assigning to 
it so vast a mass, we are not outstepping a reasonable pro- 
portion. In fact, when we come to compare its mass with 
its hulk we find its density 6 to be less than that of the earth, 
being no more than 0*2543. So that it must consist, in 
reality, of far lighter materials, especially when we consider 
the force under which its central parts must be condensed. 
This consideration renders it highly probable that an intense 
heat prevails in its interior by which its elasticity is rein- 
forced, and rendered capable of resisting this almost incon- 
ceivable pressure without collapsing into smaller dimensions. 

(450.) This will be more distinctly appreciated, if we 
estimate, as we are now prepared to do, the intensity of 
gravity at the sun's surface. 

The attraction of a sphere being the same (art. 445) as if 
its whole mass were collected in its centre, will, of course, 
pe proportional to the mass directly, and the square of the 
distance inversely; and, in this case, the distance is the 
radius of the sphere. Hence we conclude, 6 that the inten- 
sities of solar and terrestrial gravity at the surfaces of the 
two globes are in the proportions of 27*9 to 1. A pound of 
terrestrial matter at the sun's surface, then, would exert 

a pressure equal to what 27*9 such pounds would do at the 

« 

6 The density of a material body is as the mass directly, and the volume in- 
versely : hence density of : density of : : ||^ : 1 : : -2543 : 1. 

6 Solar gravity : terrestrial : :^^ : ( ^a : :2T -9 : 1 ; the respective radii of the 
Bun and earth being 440000, and 4000 miles. 



376 OUTLINES OF ASTRONOMY 

earth's. The efficacy of muscular power to overcome 
weight is therefore proportionally nearly 28 times less on 
the sun than on the earth. An ordinary man, for example, 
would not only be unable to sustain his own weight on the 
sun, but would literally be crushed to atoms under the load. 7 

(451.) Henceforward, then, we must consent to dismiss 
all idea of the earth's immobility, and transfer that attribute 
to the sun, whose ponderous mass is calculated to exhaust 
the feeble attractions of such comparative atoms as the 
earth and moon, without being perceptibly dragged from 
its place. Their centre of gravity lies, as we have already 
hinted, almost close to the centre of the solar globe, at an 
interval quite imperceptible from our distance; and whether 
we regard the earth's orbit as being performed about the one 
or the other centre makes no appreciable difference in any 
one phenomenon of astronomy. 

(452.) It is in consequence of the mutual gravitation of 
all the several parts of matter, which the Newtonian law 
supposes, that the earth and moon, while in the act of 
revolving, monthly, in their mutual orbits about their 
common centre of gravity, yet continue to circulate, with- 
out parting company, in a greater annual orbit round the 
sun. We may conceive this motion by connecting two un- 
equal balls by a short stick, which, at their common centre 
of gravity is suspended by a long string and made to gyrate 
conically round a point vertically below that of suspension. 
Their joint system will circulate as one pendulous mass 
about this imaginary centre, while yet they may go on 
circulating round each other in subordinate gyrations, as if 
the stick were quite free from any such tie, and merely 

' A mass weighing 12 stone or 168 lbs. on the earth would produce a pres- 
sure of 4681 lbs. on the sun. 



OUTLINES OF ASTRONOMY 377 

hurled through the air. If the earth alone, and not the 
moon, gravitated to the sun, it would be dragged away, 
and leave the moon behind — and vice versa ; but, acting on 
both, they continue together under its attraction, just as 
the loose parts of the earth's surface continue to rest upon 
it. It is, then, in strictness, not the earth or the moon which 
describes an ellipse around the sun, but their common 
centre of gravity. The effect is to produce a small, but 
very perceptible, monthly equation in the sun's apparent 
motion as seen from the earth, which is always taken into 
account in calculating the sun's place. The moon's actual 
path in its compound orbit round the earth and sun is an 
epicycloidal curve intersecting the orbit of the earth twice 
in -every lunar month, and alternately within and without 
it. But as there are not more than twelve such months in 
the year, and as the total departure of the moon from it 
either way does not exceed one 400th part of the radius, 
this amounts only to a slight undulation upon the earth's 
ellipse, so slight, indeed, that if drawn in true proportion 
on a large sheet of paper, no eye unaided by measurement 
with compasses would detect it. The real orbit of the moon 
is everywhere concave toward the sun. 

(453.) Here moreover, i.e. in the attraction of the sun, we 
have the key to all those differences from an exact elliptic 
movement of the moon in her monthly orbit, which we have 
already noticed (arts. 407, 409), viz. to the retrograde revo- 
lution of her nodes; to the direct circulation of the axis of 
her ellipse; and to all the other deviations from the laws 
of elliptic motion at which we have further hinted. If the 
moon simply revolved about the earth under the influence 
of its gravity, none of these phenomena would take place. 
Its orbit would be a perfect ellipse, returning into itself, 



378 OUTLINES OF ASTRONOMY 

and always lying in one and the same plane. That it is 
not so, is a proof that some cause disturbs it, and interferes 
with the earth's attraction; and this cause is no other than 
the sun's attraction — or rather, that part of it which is not 
equally exerted on the earth. 

(454.) Suppose two stones, side by side, or otherwise 
situated with respect to each other, to be let fall together; 
then, as gravity accelerates them equally, they will retain 
their relative positions, and fall together as if they formed 
one mass. But suppose gravity to be rather more intensely 
exerted on one than the other; then would that one be 
rather more accelerated in its fall, and would gradually 
leave the other; and thus a relative motion between them 
would arise from the difference of action, however slight. 

(455.) The sun is about 400 times more remote than the 
moon; and, in consequence, while the moon describes her 
monthly orbit round the earth, her distance from the sun 
is alternately 4 o th part greater and as much less than the 
earth's. Small as this is, it is yet sufficient to produce a 
perceptible excess of attractive tendency of the moon to- 
ward the sun, above that of the earth when in the nearer 

*0&! _ £fc 

point of her orbit, M, and a corresponding defect on the 
opposite part, N ; and, in the intermediate positions, not 
only will a difference of forces subsist, but a difference of 
directions also; since however small the lunar orbit M N", it 
is not a point, and, therefore, the lines drawn from the sun 
S to its several parts cannot be regarded as strictly paral- 
lel. If, as we have already seen, the force of the sun were 
equally exerted, and in parallel directions on both, no dis- , 



OUTLINES OF ASTRONOMY 379 

turbance of their relative situations would take place; but 
from the non-verification of these conditions arises a disturb- 
ing force, oblique to the line joining the moon and earth, 
which in some situations acts to accelerate, in others to 
retard, her elliptic orbitual motion; in some to draw the 
earth from the moon, in others the moon from the earth. 
Again, the lunar orbit, though very nearly, is yet not quite 
coincident with the plane of the ecliptic; and hence the 
action of the sun, which is very nearly parallel to the 
last-mentioned plane, tends to draw her somewhat out of 
the plane of her orbit, and does actually do so — producing 
the revolution of her nodes, and other phenomena less strik- 
ing. We are not yet prepared to go into the subject of 
these 'perturbations, as they are called; but they are intro- 
duced to the reader's notice as early as possible, for the 
purpose of reassuring his mind, should doubts have arisen 
as to the logical correctness of our argument, in conse- 
quence of our temporary neglect of them while working 
our way upward to the law of gravity from a general 
consideration of the moon's orbit. 



CHAPTER IX 

OF THE SOLAR SYSTEM 

Apparent Motions of the Planets — Their Stations and Retrogradations — The 
Sun their Natural Centre of Motion — Inferior Planets — Their Phases, 
Periods, etc. — Dimensions and Form of their Orbits — Transits across 
the Sun — Superior Planets — Their Distances, Periods, etc. — Kepler's 
Laws and their Interpretation — Elliptic Elements of a Planet's Orbit 
—Its Heliocentric and Geocentric Place — Empirical Law of Planetary 
Distances ; Violated in the Case of Neptune — The Asteroids — Physical 
Peculiarities Observable in each of the Planets 

(456.) The sun and moon are not the only celestial ob- 
jects which appear to have a motion independent of that 



380 OUTLINES OF ASTRONOMY 

by which the great constellation of the heavens is daily 
carried round the earth. Among the stars there are sev- 
eral — and those among the brightest and most conspicuous 
— which, when attentively watched from night to night, are 
found to change their relative situations among the rest; 
some rapidly, others much more slowly. These are called 
planets. Four of them — Venus, Mars, Jupiter and Saturn 
— are remarkably large and brilliant; another, Mercury, is 
also visible to the naked eye as a large star, but, for a 
reason which will presently appear, is seldom conspicuous : 
a sixth, Uranus, is barely so discernible, while the rest of 
which about fifty are already known, and probably many 
more remain to be discovered, are visible only through 
telescopes, 1 and with one exception (that of Neptune) can 
only be known among the multitude of minute stars those 
instruments reveal to us by watching them from night to 
night and attending to their changes of place. All these 
have been discovered since the commencement of the cur- 
rent century, and forty-five of them since 1844. A list of 
their names, discoverers, and the dates of their respective 
discovery will be found in the Appendix. All of them 
but Neptune belong to a peculiar and very remarkable 
class or family of planets to which the name of Asteroids 
has been assigned. 

(457.) The apparent motions of the planets are much 
more irregular than those of the sun or moon. Grenerally 
speaking, and comparing their places at distant times, they 
all advance, though with very different average or mean 
velocities, in the same direction as those luminaries, i.e. in 
opposition to the apparent diurnal motion, or from west 

1 One only, Vesta, is said to have been once seen by Schroter with the 
naked eye. 



OUTLINES OF ASTRONOMY 381 

to east: all of them make the entire tour of the heavens, 
though under very different circumstances: and all of them, 
with the exception of certain among the telescopic planets, 
are confined in their visible paths within very narrow limits 
on either side the ecliptic, and perform their movements 
within that zone of the heavens we have called, above, 
the Zodiac (art. 303). 

(458.) The obvious conclusion from this is, that what- 
ever be, otherwise, the nature and law of their motions, 
they are performed nearly in the plane of the ecliptic — that 
plane, namely, in which our own motion about the sun is 
performed. Hence it follows, that we see their evolutions, 
not in plan, but in section] their real angular movements and 
linear distances being all foreshortened and confounded in- 
distinguishably, while only their deviations from the eclip- 
tic appear of their natural magnitude, undiminished by the 
effect of perspective. 

(459.) The apparent motions of the sun and moon, 
though not uniform, do not deviate very greatly from 
uniformity; a moderate acceleration and retardation, ac- 
countable for by the ellipticity of their orbits, being all 
that is remarked. But the case is widely different with 
the planets: sometimes they advance rapidly; then relax 
in their apparent speed — come to a momentary stop; and 
then actually reverse their motion, and run back upon 
their former course, with a rapidity at first increasing, 
then diminishing, till the reversed or retrograde motion 
ceases altogether. Another station, or moment of apparent 
rest or indecision, now takes place ; after which the move- 
ment is again reversed, and resumes its original direct 
character. On the whole, however, the amount of direct 
motion more than compensates the retrograde; and by the 



382 OUTLINES OF ASTRONOMY 

excess of the former over the latter, the gradual advance of 
the planet from west to east is maintained. Thus, suppos- 
ing the Zodiac to be unfolded into a plane surface (or rep- 
resented as in Mercator's projection, art. 283, taking the 




ecliptic E C for its ground line), the track of a planet when 
mapped down by observation from day to day, will offer the 
appearance PQES, etc. ; the motion from P to Q being 
direct, at Q stationary, from Q to K retrograde, at K again 
stationary, from R to S direct, and so on. 

(460.) In the midst of the irregularity and fluctuation 
of this motion, one remarkable feature of uniformity is 
observed. Whenever the planet crosses the ecliptic, as at 
N in the figure, it is said (like the moon) to be in its node ; 
and as the earth necessarily lies in the plane of the ecliptic, 
the planet cannot be apparently or uranographically situated 
in the celestial circle so called, without being really and 
locally situated in that plane. The visible passage of a 
planet through its node, then, is a phenomenon indicative 
of a circumstance in its real motion quite independent of 
the station from which we view it. Now, it is easy to 
ascertain, by observation, when a planet passes from the 
north to the south side of the ecliptic: we have only to 
convert its right ascensions and declinations into longitudes 
and latitudes, and the change from north to south latitude 
on two successive days will advertise us on what day the 
transition took place ; while a simple proportion, grounded 
on the observed state of its motion in latitude in the inter- 
val, will suffice to fix the precise hour and minute of its 
arrival on the ecliptic. Now, this being done for several 



OUTLINES OF ASTRONOMY 383 

transitions from side to side of the ecliptic, and their dates 
thereby fixed, we find, universally, that the interval of time 
elapsing between the successive passages of each planet 
through the same node (whether it be the ascending or the 
descending) is always alike, whether the planet at the mo- 
ment of such passage be direct or retrograde, swift or slow, 
in its apparent movement. 

(461.) Here, then, we have a circumstance which, while 
it shows that the motions of the planets are in fact subject 
to certain laws and fixed periods, may lead us very natu- 
rally to suspect that the apparent irregularities and com- 
plexities of their movements may be owing to our not see- 
ing them from their natural centre (arts. 338, 371,) and from 
our mixing up with their own proper motions movements of 
a parallactic kind, due to our own change of place, in virtue 
of the orbital motion of the earth about the sun. 

(462.) If we abandon the earth as a centre of the planet- 
ary motions, it cannot admit of a moment's hesitation where 
we should place that centre with the greatest probability of 
truth. It must surely be the sun which is entitled to the 
first trial, as a station to which to refer to them. If it be 
not connected with them by any physical relation, it at least 
possesses the advantage, which the earth does not, of com- 
parative immobility. But after what has been shown in 
art. 449, of the immense mass of that luminary, and of the 
office it performs to us as a quiescent centre of our orbitual 
motion, nothing can be more natural than to suppose it may 
perform the same to other globes which, like the earth, may 
be revolving round it; and these globes may be visible to 
us by its light reflected from them, as the moon is. Now 
there are many facts which give a strong support to the 
idea that the planets are in this predicament. 



384 OUTLINES OF ASTRONOMY 

(463.) In the first place, the planets really are great 
globes, of a size commensurate with the earth, and several 
of them much greater. When examined through powerful 
telescopes, they are seen to be round bodies, of sensible 
and even of considerable apparent diameter, and offering 
distinct and characteristic peculiarities, which show them 
to be material masses, each possessing its individual struc- 
ture and mechanism; and that, in one instance at least, an 
exceedingly artificial and complex one. (See the represen- 
tations of Mars, Jupiter and Saturn, in Plate III.) That 
their distances from us are great, much greater than that 
of the moon, and some of them even greater than that of 
the sun, we infer, 1st, from their being occulted by the 
moon, and 2dly, from the smallness of their diurnal paral- 
lax, which, even for the nearest of them, when most favor- 
ably situated, does not exceed a few seconds, and for the 
remote ones is almost imperceptible. From the comparison 
of the diurnal parallax of a celestial body, with its appar- 
ent semidiameter, we can at once estimate its real size. For 
the parallax is, in fact, nothing else than the apparent semi- 
diameter of the earth as seen from the body in question (art. 
339 et seq.); and, the intervening distance being the same, 
the real diameters must be to each other in the proportion 
of the apparent ones. Without going into particulars, it 
will suffice to state it as a general result of that compari- 
son, that the planets are all of them incomparably smaller 
than the sun, but some of them as large as the earth, and 
others much greater. 

(464.) The next fact respecting them is, that their dis- 
tances from us, as estimated from the measurement of their 
angular diameters, are in a continual state of change, peri- 
odically increasing and decreasing within certain limits, but 



OUTLINES OF ASTRONOMY 385 

by no means corresponding with the supposition of regular 
circular or elliptic orbits described by them about the earth 
as a centre or focus, but maintaining a constant and obvious 
relation to their apparent angular distances or elongations 
from the sun. For example ; the apparent diameter of Mara 
is greatest when in opposition (as it is called) to the sun, i.e. 
when in the opposite part of the ecliptic, or when it comes 
on the meridian at midnight — being then about 18" — but 
diminishes rapidly from that amount to about 4", which is 
its apparent diameter when in conjunction, or when seen 
in nearly the same direction as that luminary. This, and 
facts of a similar character, observed with respect to the 
apparent diameters of the other planets, clearly point out 
the sun as having more than an accidental relation to their 
movements. 

(465.) Lastly, certain of the planets (Mercury, Yenus, and 
Mars), when viewed through telescopes, exhibit the appear- 
ance of phases like those of the moon. This proves that 
they are opaque bodies, shining only by reflected light, 
which can be no other than that of the sun's; not only 
because there is no other source of light external to them 
sufficiently powerful, but because the appearance and suc- 
cession of the phases themselves are (like their visible 
diameters) intimately connected with their elongations from 
the sun, as will presently be shown. 

(466.) Accordingly it is found, that, when we refer the 
planetary movements to the sun as a centre, all that ap- 
parent irregularity which they offer when viewed from the 
earth disappears at once, and resolves itself into one simple 
and general law, of which the earth's motion, as explained 
in a former chapter, is only a particular case. In order to 

show how this happens, let us take the case of a single 
Astronomy — Vol. XIX — IT 



386 OUTLINES OF ASTRONOMY 

planet, which we will suppose to revolve round the sun, in 
a plane nearly, but not quite, coincident with the ecliptic, 
but passing through the sun, and of course intersecting the 
ecliptic in a fixed line, which is the line of the planet's 
nodes. This line must of course divide its orbit into two 
segments; and it is evident that, so long as the circum- 
stances of the planet's motion remain otherwise unchanged, 
the times of describing these segments must remain the 
same. The interval, then, between the planet's quitting 
either node, and returning to the same node again, must be 
that in which it describes one complete revolution round 
the sun, or its periodic time; and thus we are furnished 
with a direct method of ascertaining the periodic time of 
each planet. 

(467.) We have said (art. 457) that the planets make 
the entire tour of the heavens under very different circum- 
stances. This must be explained. Two of them — Mercury 
and Yenus — perform this circuit evidently as attendants 
upon the sun, from whose vicinity they never depart be- 
yond a certain limit. They are seen sometimes to the east, 
sometimes to the west of it. In the former case they appear 
conspicuous over the western horizon, just after sunset, and 
are called evening stars: Yenus, especially, appears occa- 
sionally in this situation with a dazzling lustre; and in 
favorable circumstances may be observed to cast a pretty 
strong shadow. 8 When they happen to be to the west of 
the sun, they rise before that luminary in the morning, and 
appear over the eastern horizon as morning stars: they do 
not, however, attain the same elongation from the sun. 

2 It must be thrown upon a white ground. An open window in a white- 
washed room is the best exposure. In this situation I have observed not only 
the shadow, but the diffracted fringes edging its outline. — H. Note to the edi- 
tion of 1833. Venus may often be seen with the naked eye in the daytime. 



OUTLINES OF ASTRONOMY 387 

Mercury never attains a greater angular distance from it 
than about 29°, while Venus extends her excursions on 
either side to about 47°. When they have receded from 
the sun, eastward, to their respective distances, they remain 
for a time, as it were, immovable with respect to it, and are 
carried along with it in the ecliptic with a motion equal to 
its own; but presently they begin to approach it, or, which 
comes to the same, their motion in longitude diminishes, 
and the sun gains upon them. As this approach goes on, 
their continuance above the horizon after sunset becomes 
daily shorter, till at length they set before the darkness has 
become sufficient to allow of their being seen. For a time, 
then, they are not seen at all, unless on very rare occasions, 
when they are to be observed passing across the sun's dish 
as small, round, well-defined black spots, totally different in 
appearance from the solar spots (art. 386). These phenom- 
ena are emphatically called transits of the respective planets 
across the sun, and take place when the earth happens to 
be passing the line of their nodes while they are in that 
part of their orbits, just as in the account we have given 
(art. 412) of a solar eclipse. After having thus continued 
invisible for a time, however, they begin to appear on the 
other side of the sun, at first showing themselves only for 
a few minutes before sunrise, and gradually longer and 
longer as they recede from him. At this time their motion 
in longitude is rapidly retrograde. Before they attain their 
greatest elongation, however, they become stationary in the 
heavens; but their recess from the sun is still maintained 
by the advance of that luminary along the ecliptic, which 
continues to leave them behind, until, having reversed 
their motion, and become again direct, they acquire suffi- 
cient speed to commence overtaking him — at which moment 



388 OUTLINES OF ASTRONOMY 

they have their greatest western elongation; and thus is a 
kind of oscillatory movement kept up, while the general 
advance along the ecliptic goes on. 

(468.) Suppose P Q to be the ecliptic, and A B C D the 
orbit of one of these planets (for instance, Mercury), seen 
almost edgewise by an eye situated very nearly in its plane; 
S, the sun, its centre; and A, B, C, D successive positions 
of the planet, of which B and D are in the nodes. If, then, 
the sun S stood apparently still in the ecliptic, the planets 
would simply appear to oscillate backward and forward 
from A to C, alternately passing before and behind the 
sun; and, if the eye happened to lie exactly in the plane 
of the orbit, transiting his disk in the former case, and 
being covered by it in the latter. But as the sun is not so 




stationary, but apparently carried along the ecliptic P Q, 
let it be supposed to move over the spaces S T, T U, U V, 
while the planet in each case executes one quarter of its 
period. Then will its orbit be apparently carried along 
with the sun, into the successive positions represented in 
the figure; and while its real motion round the sun brings 
it into the respective points, B, C, D, A, its apparent move- 
ment in the heavens will seem to have been along the wavy 
or zigzag line ANHK, In this, its motion in longitude 
will have been direct in the parts A N, N H, and retrograde 
in the parts H n K ; while at the turns of the zigzag, as at 
H, it will have been stationary. 

(469.) The only two planets — Mercury and Venus — 
whose evolutions are such as above described, are called 



OUTLINES OF ASTRONOMY 389 

inferior planets; their points of furthest recess from the sun 
are called (as above) their greatest eastern and western elon- 
gations; and their points of nearest approach to it, their 
inferior and superior conjunctions — the former when the 
planet passes between the earth and the sun, the latter 
when behind the sun. 

(470.) In art. 467 we have traced the apparent path of 
an inferior planet, by considering its orbit in section, or 
as viewed from a point in the plane of the ecliptic. Let 
us now contemplate it in plan, or as viewed from a station 
above that plane, and projected on it. Suppose then, S 
to represent the sun, abed the orbit 
of Mercury, and A B C D a part of 
that of the earth — the direction of the 
circulation being the same in both, viz. 
that of the arrow. When the planet 
stands at a, let the earth be situated at ^ 

A, in the direction of a tangent, a A, to its orbit; then it is 
evident that it will appear at its greatest elongation from 
the sun — the angle a A S, which measures their apparent 
interval as seen from A, being then greater than in any 
other situation of a upon its own circle. 

(471.) Now, this angle being known by observation, we 
are hereby furnished with a ready means of ascertaining, 
at least approximately, the distance of the planet from the 
sun, or the radius of its orbit, supposed a circle. For the 
triangle S A a is right-angled at a, and consequently we 
have S a : S A : : sin. S A a : radius, by which proportion 
the radii S a, S A of the two orbits are directly compared. 
If the orbits were both exact circles, this would of course 
be a perfectly rigorous mode of proceeding: but (as is 
proved by the inequality of the resulting values of S a ob- 




690 OUTLINES OF ASTRONOMY 

tained at different times) this is not the case ; and it becomes 
necessary to admit an excentricity of position, and a devia- 
tion from the exact circular form in both orbits, to account 
for this difference. Neglecting, however, at present this 
inequality, a mean or average value of S a may, at least, 
be obtained from the frequent repetition of this process in 
all varieties of situation of the two bodies. The calculations 
being performed, it is concluded that the mean distance of 
Mercury from the sun is about 36000000 miles; and that 
of Venus, similarly derived, about 68000000; the radius of 
the earth's orbit being 95000000. 

(472.) The sidereal periods of the planets may be ob- 
tained (as before observed), with a considerable approach 
to accuracy, by observing their passages through the nodes 
of their orbits; and indeed, when a certain very minute 
motion of these nodes and the apsides of their orbits (similar 
to that of the moon's nodes and apsides, but incomparably 
slower) is allowed for, with a precision only limited by the 
imperfection of the appropriate observations. By such ob- 
servation, so corrected, it appears that the sidereal period 
of Mercury is 87 d 23 h 15 m 43 -9 s ; and that of Yen us, 224 d 
16 h 49 m 8*0 8 . These periods, however, are widely different 
from the intervals at which the successive appearances of 
the two planets at their eastern and western elongations 
from the sun are observed to happen. Mercury is seen at 
its greatest splendor as an evening star, at average intervals 
of about 116, and Venus at intervals of about 584 days. The 
difference between the sidereal and synodical revolutions (art. 
418) accounts for this. Eeferring again to the figure of art. 
470, if the earth stood still at A, while the planet advanced 
in its orbit, the lapse of a sidereal period, which should 
bring it round again to a, would also produce a similar 



OUTLINES OF ASTRONOMY 391 

elongation from the sun. But, meanwhile, the earth has 
advanced in its orbit in the same direction toward E, and 
therefore the next greatest elongation on the same side of 
the sun will happen — not in the position a A of the two 
bodies, but in some more advanced position, e E. The 
determination of this position depends on a calculation 
exactly similar to what has been explained in the article 
referred to; and we need, therefore, only here state the 
resulting synodical revolutions of the two planets, which 
come out respectively 115'877 d , and 583'920 d . 

(473.) In this interval, the planet will have described a 
whole revolution plus the arc ace, and the earth only the 
arc A C E of its orbit. During its lapse, the inferior con- 
junction will happen when the earth has a certain inter- 
mediate situation, B, and the planet has reached 6, a point 
between the sun and earth. The greatest elongation on the 
opposite side of the sun will happen when the earth has 
come to C, and the planet to c, where the line of junction 
C c is a tangent to the interior circle on trie opposite side 
from M. Lastly, the superior conjunction will happen when 
the earth arrives at D, and the planet at d in the same line 
prolonged on the other side of the sun. The intervals at 
which these phenomena happen may easily be computed 
from a knowledge of the synodical periods and the radii 
of the orbits. 

(474.) The circumferences of circles are in the proportion 
of their radii. If, then, we calculate the circumferences of 
the orbits of Mercury and Yenus, and trie earth, and com- 
pare them with the times in which their revolutions are 
performed, we shall find that the actual velocities with 
which they move in their orbits differ greatly; that of 
Mercury being about 109360 miles per hour, of Yenus 



392 OUTLINES OF ASTRONOMY 

80000, and of the earth 68040. From this it follows, that 
at the inferior conjunction, or at b, either planet is moving 
in the same direction as the earth, but with a greater veloc- 
ity; it will, therefore, leave the earth behind it; and the 
apparent motion of the planet viewed from the earth, will 
be as if the planet stood still, and the earth moved in a 
contrary direction from what it really does. In this situa- 
tion, then, the apparent motion of the planet must be con- 
trary to the apparent motion of the sun; and, therefore, 
retrograde. On the other hand, at the superior conjunc- 
tion, the real motion of the planet being in the opposite 
direction to that of the earth, the relative motion will be 
the same as if the planet stood still, and the earth advanced 
with their united velocities in its own proper direction. In 
this situation, then, the apparent motion will be direct. 
Both these results are in accordance with observed fact. 
(475. ) The stationary points may be determined by the 
following consideration. At a or c, the points of greatest 
elongation, the motion of the planet is directly to or from 
the earth, or along their line of junction, while that of the 
earth is nearly perpendicular to it. Here, then, the appar- 
ent motion must be direct. At 6, the inferior conjunction, 
we have seen that it must be retrograde, owing to the 
planet's motion (which is there, as well as the earth's, per- 
pendicular to the line of junction) surpassing the earth's. 
Hence, the stationary points ought to lie, as it is found 
by observation they do, between a and b, or c and Z>, viz. 
in such a position that the obliquity of the planet's motion 
with respect to the line of junction shall just compensate 
for. the excess of its velocity, and cause an equal advance 
of each extremity of that line, by the motion of the planet 
at one end, and of the earth at the other: so that, for an 



OUTLINES OF ASTRONOMY 



393 



instant of time, the whole line shall move parallel to itself. 
The question thus proposed is purely geometrical, and its 
solution on the supposition of circular orbits is easy. Let 
E e and P p represent small arcs of the orbits of the earth 
and planet described contemporaneously, at the moment 
when the latter appears stationary, about S, the sun. Pro- 




duce p P and e E, tangents at P and E, to meet at E, and 
prolong E P backward to Q, join e p. Then since P E, 
p e are parallel we have by similar triangles P p : E e : : 
P E : R E, and since, putting v and Y for the respective 
velocities of the planet and the earth, Pj):Ee::v:V; 
therefore 

v:V::PK:RE:: sin. PER: sin. EPR 
: : cos. SEP: cos. S P Q 
: : cos. SEP: cos. (S E P + E S P) 
because the angles SER and SPR are right angles. 
Moreover, if r and R be the radii of the respective orbits, 
we have also 

r : R : : sin. SEP: sin. (S E P + E S P) 
from which two relations it is easy to deduce the values 



394 OUTLINES OF ASTRONOMY 

of the two angles SEP and ESP; the former of which 
is the apparent elongation of the planet from the sun, 8 the 
latter the difference of heliocentric longitudes of the earth 
and planet. 

(476.) When we regard the orbits as other than circles 
(which they really are), the problem becomes somewhat 
complex — too much so to be here entered upon. It will 
suffice to state the results which experience verifies, and 
which assign the stationary points of Mercury at from 
15° to 20° of elongation from the sun, according to cir- 
cumstances ; and of Yenus, at an elongation never varying 
much from 29°. The former continues to retrograde during 
about 22 days; the latter, about 42. 

(477.) We have said that some of the planets exhibit 
phases like the moon. This is the case with both Mercury 
and Yenus; and is readily explained by a consideration of 
their orbits, such as we have above supposed them. In 

fact, it requires little more 
than mere inspection of the 
figure annexed, to show, 
that to a spectator situated 
on the earth E, an inferior 
planet, illuminated by the 
sun, and therefore bright 
on the side next to him, and dark on that turned from 
him, will appear full at the superior conjunction A; 
gibbous (i.e. more than half full, like the moon between 
the first and second quarter) between that point and the 




T» ~y 

3 If _ == m and— «=w, S E P=<£, E S P= ^, the equations to be resolved are 
r v 

1+mn 
in. (<t> + +)~m sin. $, and cos. (^-H*) n cos. f, which gives cos. *— ~^£ n ~ 



OUTLINES OF ASTRONOMY 395 

points B C of its greatest elongation; half -mooned at these 
points; and crescent-shaped, or horned, between these and 
the inferior conjunction D. As it approaches this point, 
the crescent ought to thin off till it vanishes altogether, 
rendering the planet invisible, unless in those cases where 
it transits the sun's disk, and appears on it as a black 
spot. All these phenomena are exactly conformable to 
observation. 

(478.) The variation in brightness of Yenus in different 
parts of its apparent orbit is very remarkable. This arises 
from two causes: 1st, the varying proportion of its visible 
illuminated area to its whole disk; and, 2dly, the varying 
angular diameter, or whole apparent magnitude of the disk 
itself. As it approaches its inferior conjunction from its 
greater elongation, the half-moon becomes a crescent, which 
thins off; but this is more than compensated, for some time, 
by the increasing apparent magnitude, in consequence of its 
diminishing distance. Thus the total light received from 
it goes on increasing, till at length it attains a maximum, 
which takes place when the planet's elongation is about 40°. 

(479.) The transits of Yenus are of very rare occurrence, 
taking place alternately at the very unequal but regularly 
recurring intervals of 8, 122, 8, 105, 8, 122, etc., years in 
succession, and always in June or December. As astro- 
nomical phenomena, they are extremely important; since 
they afford the best and most exact means we possess of 
ascertaining the sun's distance, or its parallax. Without 
going into the niceties of calculation of this problem, 
which, owing to the great multitude of circumstances to 
be attended to, are extremely intricate, we shall here ex- 
plain its principle, which, in the abstract, is very simple 
and obvious. Let E be the earth, Y Yenus, and S the 



396 OUTLINES OF ASTRONOMY 

sun, and C D the portion of Venus 's relative orbit which 
she describes while in the act of transiting the sun's disk. 
Suppose A B two spectators at opposite extremities of that 
diameter of the earth which is perpendicular to the ecliptic, 
and, to avoid complicating the case, let us lay out of con- 
sideration the earth's rotation, and suppose A, B, to retain 
that situation during the whole time of the transit. Then, 
at any moment when the spectator at A sees the centre of 
Venus projected at a on the sun's disk, he at B will see 
it projected at b. If then one or other spectator could sud- 
denly transport himself from A to B, he would see Venus 
suddenly displaced on the disk from a to b; and if he had 
any means of noting accurately the place of the points on 




the disk, either by micrometrical measures from its edge, 
or by other means, he might ascertain the angular measure 
of a b as seen from the earth. Now, since A V a, B V b 1 
are straight lines, and therefore make equal angles on each 
side V, a b will be to A B as the distance of Venus from 
the sun is to its distance from the earth, or as 68 to 27, or 
nearly as 2J to 1; a b therefore occupies on the sun's disk 
a space 2£ times as great as the earth's diameter; and its 
angular measure is therefore equal to about 2-J- times the 
earth's apparent diameter at the distance of the sun, or 
(which is the same thing) to five times the sun's horizontal 
parallax (art. 298). Any error, therefore, which may be 
committed in measuring a b, will entail only one-fifth of 
that error on the horizontal parallax concluded from it. 



OUTLINES OF ASTRONOMY 397 

(480.) The thing to be ascertained, therefore, is, in fact, 
neither more nor less than the breadth of the zone PQES, 
p q r 5, included between the extreme apparent paths of the 
centre of Yenus across the sun's disk, from its entry on one 
side to its quitting it on the other. The whole business of 
the observers at A, B, therefore, resolves itself into this; 
— to ascertain, with all possible care and precision, each at 
his own station, this path — where it enters, where it quits, 
and what segment of the sun's disk it cuts off. Now, one 
of the most exact ways in which (conjoined with careful 
micrometric measures) this can be done, is by noting the 
time occupied in the whole transit: for the relative angular 
motion of Yenus being, in fact, very precisely known from 
the tables of her motion, and the apparent path being very 
nearly a straight line, these times give us a measure (on a 
very enlarged scale) of the lengths of the chords of the seg- 
ments cut off; and the sun's diameter being known also 
with great precision, their versed sines, and therefore their 
difference, or the breadth of the zone required, becomes 
known. To obtain these times correctly, each observer 
must ascertain the instants of ingress and egress of the 
centre. To do this, he must note, 1st, the instant when 
the first visible impression or notch on the edge of the 
disk at P is produced, or the first external contact] 2dly, 
when the planet is just wholly immersed, and the broken 
edge of the disk just closes again at Q, or the first internal 
contact; and, lastly, he must make the same observations at 
the egress at E, S. The mean of the internal and external 
contacts, corrected for the curvature of the sun's limb in 
the intervals of the respective points of contact, internal 
and external, gives the entry and egress of the planet's 
centre. 



398 OUTLINES OF ASTRONOMY 

(481.) The modifications introduced into this process by 
the earth's rotation on its axis, and by other geographical 
stations of the observers thereon than here supposed, are 
similar in their principles to those which enter into the 
calculation of a solar eclipse,^ or the occultation of a star 
by the moon, only more refined. Any consideration of 
them, however, here, would lead us too far; but in the 
view we have taken of the subject, it affords an admirable 
example of the way in which minute elements in astronomy 
may become magnified in their effects, and, by being made 
subject to measurement on a greatly enlarged scale, or by 
substituting the measure of time for space, may be ascer- 
tained with a degree of precision adequate to every purpose, 
by only watching favorable opportunities, and taking ad- 
vantage of nicely adjusted combinations of circumstance. 
So important has this observation appeared to astronomers, 
that at the last transit of Venus, in 1769, expeditions were 
fitted out, on the most efficient scale, by the British, French, 
Russian, and other governments, to the remotest corners of 
the globe, for the express purpose of performing it. The 
celebrated expedition of Captain Cook to Otaheite was one 
of them. The general result of all the observations made 
on this most memorable occasion gives 8*577.6 for the sun's 
horizontal parallax. The next two occurrences of this phe- 
nomenon will happen on December 8, 1874, and December 
6, 1882. [See Note F, § 357 b b.] 

(482.) The orbit of Mercury is very elliptical, the ex- 
centricity being nearly one-fourth of the mean distance. 
This appears from the inequality of the greatest elongations 
from the sun, as observed at different times, and which vary 
between the limits 16° 12' and 28° 48', and, from exact meas- 
ures of such elongations, it is not difficult to show that the 



OUTLINES OF ASTRONOMY 399 

orbit of Venus also is slightly excentric, and that both these 
planets, in fact, describe ellipses, having the sun in their 
common focus. 

(483.) Transits of Mercury over the sun's disk occasion- 
ally occur, as in the case of Yenus, but more frequently; 
those at the ascending node in November, at the descending 
in May. The intervals (considering each node separately) 
are usually either 13 or 7 years, and in the order 13, 13, 
13, 7, etc. ; but owing to the considerable inclination of the 
orbit of Mercury to the ecliptic, this cannot be taken as 
an exact expression of the said recurrence, and it requires 
a period of at least 217 years to bring round the transits in 
regular order. One will occur in the present year (1848), 
the next in 1861. They are of much less astronomical im- 
portance than that of Yenus, on account of the proximity 
of Mercury to the sun, which affords a much less favorable 
combination for the determination of the sun's parallax. 

(484.) Let us now consider the superior planets, or those 
whose orbits inclose on all sides that of the earth. That 
they do so is proved by several circumstances: — 1st, They 
are not, like the inferior planets, confined to certain limits 
of elongation from the sun, but appear at all distances from 
it, even in the opposite quarter of the heavens, or, as it is 
called, in opposition; which could not happen, did not the 
earth at such times place itself between them and the sun: 
2dly, They never appear horned, like Yenus or Mercury, 
nor even semilunar. Those, on the contrary, which, from 
the minuteness of their parallax, we conclude to be the 
most distant from us, viz. Jupiter, Saturn, Uranus, and 
Neptune, never appear otherwise than round; a sufficient 
proof, of itself, that we see them always in a direction not 
very remote from that in which the sun's rays illuminate 



400 OUTLINES OF ASTRONOMY 

them; and that, therefore, we occupy a station which is 
never very widely removed from the centre of their orbits, 
or, in other words, that the earth's orbit is entirely inclosed 
within theirs, and of comparatively small diameter. One 
only of them, Mars, exhibits any perceptible phase, and in 
its deficiency from a circular outline, never surpasses a 
moderately gibbous appearance — the enlightened portion of 
the disk being never less than seven-eighths of the whole. 
To understand this, we need only cast our 
eyes on the annexed figure, in which E is 
) e the earth, at its apparent greatest elongation 
from the sun S, as seen from Mars, M. In 
this position, the angle S M E, included 
between the lines S M and E M, is at its 
maximum; and therefore, in this state of 
things, a spectator on the earth is enabled 
to see a greater portion of the dark hemi- 
sphere of Mars than in any other situation. 
The extent of the phase, then, or greatest 
observable degree of gibbosity, affords a measure — a sure, 
although a coarse and rude one — of the angle S M E, and 
therefore of the proportion of the distance S M, of Mars, 
to S E, that of the earth from the sun, by which it appears 
that the diameter of the orbit of Mars cannot be less than 1\ 
times that of the earth's. The phases of Jupiter, Saturn, 
Uranus, and Neptune, being imperceptible, it follows that 
their orbits must include not only that of the earth, but of 
Mars also. 

(485.) All the superior planets are retrograde in their 
apparent motions when in opposition, and for some time 
before and after; but they differ greatly from each other, 
both in the extent of their arc of retrogradation, in the 




OUTLINES OF ASTRONOMY 401 

duration of their retrograde movement, and in its rapidity 
when swiftest. It is more extensive and rapid in the case 
of Mars than of Jupiter, of Jupiter than of Saturn, of that 
planet than of Uranus, and of Uranus again than Neptune. 
The angular velocity with which a planet appears to retro- 
grade is easily ascertained by observing its apparent place 
in the heavens from day to day ; and from such observa- 
tions, made about the time of opposition, it is easy to con- 
clude the relative magnitudes of their orbits, as compared 
with the earth's, supposing their periodical times known. 
For, from these, their mean angular velocities are known 
also, being inversely as the times. Suppose, then, E e to 
be a very small portion of the earth's orbit, and M m a cor- 
responding portion of that of a superior planet, described 



on the day of opposition, about the sun S, on which day 
the three bodies lie in one straight line S E M X. Then 
the angles ESe and M S m are given. Now, if e m be 
joined and prolonged to meet S M continued in X, the 
angle e X E, which is equal to the alternate angle X e Y, 
is evidently the retrogradation of Mars on that day, and 
is, therefore, also given. E e, therefore, and the angle EXe, 
being given in the right-angled triangle E e X, the side 
E X is easily calculated, and thus S X becomes known. 
Consequently, in the triangle S m X, we have given the 
side S X and the two angles m S X, and m X S, whence 
the other sides, S m, m X, are easily determined. Now, 
S m is no other than the radius of the orbit of the superior 
planet required, which in this calculation is supposed cir- 
cular, as well as that of the earth ; a supposition not exact, 



402 OUTLINES OF ASTRONOMY 

but sufficiently so to afford a satisfactory approximation to 
the dimensions of its orbit, and which, if the process be 
often repeated, in every variety of situation at which the 
opposition can occur, will ultimately afford an average or 
mean value of its diameter fully to be depended upon. 

(486.) To apply this principle, however, to practice, it is 
necessary to know the periodic times of the several planets. 
These may be obtained directly, as has been already stated, 
by observing the intervals of their passages through the 
ecliptic; but, owing to the very small inclination of the 
orbits of some of them to its plane, they cross it so obliquely 
that the precise moment of their arrival on it is not ascer- 
tainable, unless by very nice observations. A better method 
consists in determining, from the observations of several 
successive days, the exact moments of their arriving in 
opposition with the sun, the criterion of which is a differ- 
ence of longitudes between the sun and planet of exactly 
180°. The interval between successive oppositions thus 
obtained is nearly one synodical period; and would be ex- 
actly so, were the planet's orbit and that of the earth both 
circles, and uniformly described; but as that is found not 
to be the case (and the criterion is, the inequality of suc- 
cessive synodical revolutions so observed), the average of 
a great number, taken in all varieties of situation in which 
the oppositions occur, will be freed from the elliptic in- 
equality, and may be taken as a mean synodical period. 
From this, by the considerations and by the process of cal- 
culation, indicated (art. 418) the sidereal periods are readily 
obtained. The accuracy of this determination will, of course, 
be greatly increased by embracing a long interval between 
the extreme observations employed. In point of fact, that 
interval extends to nearly 2000 years in the cases of the 



OUTLINES OF ASTRONOMY 403 

planets known to the ancients, who have recorded their 
observations of them in a manner sufficiently careful to be 
made use of. Their periods may, therefore, be regarded as 
ascertained with the utmost exactness. Their numerical 
values will be found stated, as well as the mean distances, 
and all the other elements of the planetary orbits, in the 
synoptic table at the end of the volume, to which (to avoid 
repetition) the reader is once for all referred. 

(487.) In casting our eyes down the list of the planetary 
distances, and comparing them with the periodic times, we 
cannot but be struck with a certain correspondence. The 
greater the distance, or the larger the orbit, evidently the 
longer the period. The order of the planets, beginning from 
the sun, is the same, whether we arrange them according to 
their distances, or to the time they occupy in completing 
their revolutions; and is as follows: — Mercury, Venus, 
Earth, Mars, the recently discovered family of Asteroids, 
Jupiter, Saturn, Uranus, and Neptune. Nevertheless, when 
we come to examine the numbers expressing them, we find 
that the relation between the two series is not that of simple 
proportional increase. The periods increase more than in 
proportion to the distances. Thus, the period of Mercury 
is about 88 days, and that 'of the Earth 365 — being in pro- 
portion as 1 to 4*15, while their distances are in the less 
proportion of 1 to 2*56; and a similar remark holds good 
in every instance. Still, the ratio of increase of the times 
is not so rapid as that of the squares of the distances. The 
square of 2-56 is 6*5536, which is considerably greater than 
4-15. An intermediate rate of increase, between the simple 
proportion of the distances and that of their squares, is there- 
fore clearly pointed out by the sequence of the numbers; 
but it required no ordinary penetration in the illustrious 



404 OUTLINES OF ASTRONOMY 

Kepler, backed by uncommon perseverance and industry, 
at a period when the data themselves were involved in 
obscurity, and when the processes of trigonometry and of 
numerical calculation were encumbered with difficulties, 
of which the more recent invention of logarithmic tables 
has happily left us no conception, to perceive and demon- 
strate the real law of their connection. This connection 
is expressed in the following proposition: — "The squares 
of the periodic times of any two planets are to each other, 
in the same proportion as the cubes of their mean distances 
from the sun." Take, for example, the Earth and Mars, 4 
whose periods are in the proportion of 3652564 to 6869796, 
and whose distance from the sun is that of 100000 to 152369; 
and it will be found, by any one who will take the trouble 
to go through the calculation, that — 

(3652564) 2 : (6869796)* :: (100000) 9 : (152369) 3 . 
(488.) Of all the laws to which induction from pure 
observation has ever conducted man, this third law (as it 
is called) of Kepler may justly be regarded as the most 
remarkable, and the most pregnant with important conse- 
quences. When we contemplate the constituents of the 
planetary system from the point of view which this rela- 
tion affords us, it is no longer mere analogy which strikes 
us — no longer a general resemblance among them, as indi- 
viduals independent of each other, and circulating about 
the sun, each according to its own peculiar nature, and 
connected with it by its own peculiar tie. The resem- 
blance is now perceived to be a true family likeness ; they 
are bound up in one chain — interwoven in one web of 

4 The expression of this law of Kepler requires a slight modification when 
we come to the extreme nicety of numerical calculation, for the greater planets, 
due to the influence of their masses. This correction is imperceptible for the 
Earth and Mars. 



OUTLINES OF ASTRONOMY 405 

mutual relation and harmonious agreement — subjected to 
one pervading influence, which extends from the centre 
to the furthest limits of that great system, of which all 
of them, the earth included, must henceforth be regarded 
as members. 

(489.) The laws of elliptic motion about the sun as a 
focus, and of the equable description of areas by lines 
joining the sun and planets, were originally established 
by Kepler, from a consideration of the observed motions 
of Mars; and were by him extended, analogically, to all 
the other planets. However precarious such an extension 
might then have appeared, modern astronomy has com- 
pletely verified it as a matter of fact, by the general co- 
incidence of its results with entire series of observations 
of the apparent places of the planets. These are found 
to accord satisfactorily with the assumption of a particular 
ellipse for each planet, whose magnitude, degree of excen- 
tricity, and situation in space, are numerically assigned in 
the synoptic table before referred to. It is true, that when 
observations are carried to a high degree of precision, and 
when each planet is traced through many successive revo- 
lutions, and its history carried back, by the aid of calcula- 
tions founded on these data, for many centuries, we learn 
to regard the laws of Kepler as only first approximations to 
the much more complicated ones which actually prevail; 
and that to bring remote observations into rigorous and 
mathematical accordance with each other, and at the same 
time to retain the extremely convenient nomenclature and 
relations of the elliptic system, it becomes necessary to 
modify, to a certain extent, our verbal expression of the 
laws, and to regard the numerical data, or elliptic elements 
of the planetary orbits as not absolutely permanent, but 



406 OUTLINES OF ASTRONOMY 

subject to a series of extremely slow and almost impercep- 
tible changes. These changes may be neglected when we 
consider only a few revolutions; but going on from century 
to century, and continually accumulating, they at length 
produce material departures in the orbits from their original 
state. Their explanation will form the subject of a subse- 
quent chapter; but for the present we must lay them out 
of consideration, as of an order too minute to affect the 
general conclusions with which we are now concerned. By 
what means astronomers are enabled to compare the results 
of the elliptic theory with observation, and thus satisfy 
themselves of its accordance with nature, will be explained 
presently, 

(490.) It will first, however, be proper to point out what 
particular theoretical conclusion is involved in each of the 
three laws of Kepler, considered as satisfactorily established 
— what indication each of them, separately, affords of the 
mechanical forces prevalent in our system, and the mode 
in which its parts are connected — and how, when thus con- 
sidered, they constitute the basis on which the Newtonian 
explanation of the mechanism of the heavens is mainly sup- 
ported. To begin with the first law, that of the equable de- 
scription of areas.- — Since the planets move in curvilinear 
paths, they must (if they be bodies obeying the laws of 
dynamics) be deflected from their otherwise natural recti- 
linear progress . by force. And from this law, taken as a 
matter of observed fact, it follows, that the direction of such 
force, at every point of the orbit of each planet, always 
passes through the sun. No matter from what ultimate 
cause the power which is called gravitation originates — be 
it a virtue lodged in the sun as its receptacle, or be it 
pressure from without, or the resultant of many pressures 



OUTLINES OF ASTRONOMY 407 

or solicitations of unknown fluids, magnetic or electric 
ethers, or impulses — still, when finally brought under our 
contemplation, and summed up into a single resultant en- 
ergy — its direction is, from every point on all sides, toward 
the suns centre. As an abstract dynamical proposition, the 
reader will find it demonstrated by Newton, in the first 
proposition of the Principia, with an elementary simplicity 
to which we really could add nothing but obscurity by am- 
plification, that any body, urged toward a certain central 
point by a force continually directed thereto, and thereby 
deflected into a curvilinear path, will describe about that 
centre equal areas in equal times; and vice versa, that such 
equable description of areas is itself the essential criterion 
of a continual direction of the acting force toward the 
centre to which this character belongs. The first law of 
Kepler, then, gives us no information as to the nature 
or intensity of the force urging the planets to the sun ; the 
only conclusion it involves is, that it does so urge them. 
It is a property of orbital rotation under the influence of 
central forces generally, and, as such, we daily see it exem- 
plified in a thousand familiar instances. A similar experi- 
mental illustration of it is to tie a bullet to a thin string, 
and, having whirled it round with a moderate velocity in 
a vertical plane, to draw the end of the string through a 
small ring, or allow it to coil itself round the finger, or 
round a cylindrical rod held very firmly in a horizontal 
position. The bullet will then approach the centre of 
motion in a spiral line; and the increase of its angular 
velocity, and the rapid diminution of its periodic time when 
near the centre, will express, more clearly than any words, 
the compensation by which its uniform description of areas 
is maintained under a constantly diminishing distance. If 



408 OUTLINES OF ASTRONOMY 

the motion be reversed, and the thread allowed to uncoil, 
beginning with a rapid impulse, the angular velocity will 
diminish by the same degrees as it before increased. The 
increasing rapidity of a dancer's pirouette, as he draws in 
his limbs and straightens his whole person, so as to bring 
every part of his frame as near as possible to the axis 
of his motion, is another instance where the connection of 
the observed effect with the central force exerted, though 
equally real, is much less obvious. 

(491.) The second law of Kepler, or that which asserts 
that the planets describe ellipses about the sun as their 
focus, involves, as a consequence, the law of solar gravi- 
tation (so be it allowed to call the force, whatever it be, 
which urges them toward the sun) as exerted on each in- 
dividual planet, apart from all connection with the rest. A 
straight line, dynamically speaking, is the only path which 
can be pursued by a body absolutely free, and under the ac- 
tion of no external force. All deflection into a curve is evi- 
dence of the exertion of a force ; and the greater the deflec- 
tion in equal times, the more intense the force. Deflection 
from a straight line is only another word for curvature of 
path; and as a circle is characterized by the uniformity 
of its curvatures in all its parts — so is every other curve 
(as an ellipse) characterized by the particular law which 
regulates the increase and diminution of its curvature as 
we advance along its circumference. The deflecting force, 
then, which continually bends a moving body into a curve, 
may be ascertained, provided its direction, in the first place, 
and, secondly, the law of curvature of the curve itself, be 
known. Both these enter as elements into the expression 
of the force. A body may describe, for instance, an ellipse, 
under a great variety of dispositions of the acting forces: it 



OUTLINES OF ASTRONOMY 409 

may glide along it, for example, as a bead upon a polished 
wire, bent into an elliptic form; in which case the acting 
force is always perpendicular to the wire, and the velocity 
is uniform. In this case the force is directed to no fixed 
centre, and there is no equable description of areas at all. 
Or it may describe it as we may see done, if we suspend 
a ball by a very long string, and, drawing it a little aside 
from the perpendicular, throw it round with a gentle im- 
pulse. In this case the acting force is directed to the centre 
of the ellipse, about which areas are described equably, and 
to which a force proportional to the distance (the decom- 
posed result of terrestrial gravity) perpetually urges it.* 
This is at once a very easy experiment, and a very in- 
structive one, and we shall again refer to it. In the case 
before us, of an ellipse described by the action of a force 
directed to the focus, the steps of the investigation of the 
law of force are these: 1st, The law of the areas determines 
the actual velocity of the revolving body at every point, or 
the space really run over by it in a given minute portion 
of time; 2dly, The law of curvature of the ellipse deter- 
mines the linear amount of deflection from the tangent in 
the direction of the focus, which corresponds to that space so 
run over; 3dly, and lastly, The laws of accelerated motion 
declare that the intensity of the acting force causing such 
deflection in its own direction, is measured by or propor- 
tional to the amount of that deflection, and may therefore 
be calculated in any particular position, or generally ex- 
pressed by geometrical or algebraic symbols, as a law inde- 
pendent of particular positions, when that deflection is so 

5 If the suspended body be a vessel full of fine sand, having a small hole at 
its bottom, the elliptic trace of its orbit will be left in a sand streak on a table 
placed below it. This neat illustration is due, to the best of my knowledge, 
to Mr. Babbage. 

Astronomy — Vol. XIX— 18 



410 OUTLINES OF ASTRONOMY 

calculated or expressed. We have here the spirit of the 
process by which Newton has resolved this interesting 
problem. For its geometrical detail, we must refer to the 
3d section of his Principia. We know of no artificial mode 
of imitating this species of elliptic motion; though a rude 
approximation to it — enough, however, to give a conception 
of the alternate approach and recess of the revolving body 
to and from the focus, and the variation of its velocity — 
may be had by suspending a small steel bead to a fine and 
very long silk fibre, and setting it to revolve in a small 
orbit round the pole of a powerful cylindrical magnet, held 
upright, and vertically under the point of suspension. 

(492.) The third law of Kepler, which connects the dis- 
tances and periods of the planets by a general rule, bears 
with it, as its theoretical interpretation, this important con- 
sequence, viz. that it is one and the same force, modified 
only by distance from the sun, which retains all the planets 
in their orbits about it. That the attraction of the sun (if 
such it be) is exerted upon all the bodies of our system in- 
diiferently, without regard to the peculiar materials of which 
they may consist, in the exact proportion of their inertias, or 
quantities of matter; that it is not, therefore, of the nature 
of the elective attractions of chemistry or of magnetic action, 
which is powerless on other substances than iron and some 
one or two more, but is of a more universal character, and 
extends equally to all the material constituents of our sys- 
tem, and (as we shall hereafter see abundant reason to admit) 
to those of other systems than our own. This law, impor- 
tant and general as it is, results, as the simplest of corolla- 
ries, from the relations established by Newton in the section 
of the Principia referred to (Prop, xv.), from which propo- 
sition it results, that if the earth were taken from its actual 



OUTLINES OF ASTRONOMY 411 

orbit, and launched anew in space at the place, in the direc- 
tion, and with the velocity of any of the other planets, it 
would describe the very same orbit, and in the same period, 
which that planet actually does, a minute correction of the 
period only excepted, arising from the difference between 
the mass of the earth and that of the planet. Small as the 
planets are compared to the sun, some of them are not, as 
the earth is, mere atoms in the comparison. The strict 
wording of Kepler's law, as Newton has proved in his fifty- 
ninth proposition, is applicable only to the case of planets 
whose proportion to the central body is absolutely inappre- 
ciable. When this is not the case, the periodic time is 
shortened in the proportion of the square root of the num- 
ber expressing the sun's mass or inertia, to that of the sum 
of the numbers expressing the masses of the sun and planet; 
and in general, whatever be the masses of two bodies revolv- 
ing round each other under the influence of the Newtonian 
law of gravity, the square of their periodic time will be ex- 
pressed by a fraction whose numerator is the cube of their 
mean distance, i.e. the greater semi- axis of their elliptic 
orbit, and whose denominator is the sum of their masses. 
When one of the masses is incomparably greater than the 
other, this resolves into Kepler's law; but when this is not 
the case, the proposition thus generalized stands in lieu of 
that law. In the system of the sun and planets, however, 
the numerical correction thus introduced into the results of 
Kepler's law is too small to be of any importance, the mass 
of the largest of the planets (Jupiter) being much less than a 
thousandth part of that of the sun. We shall presently, 
however, perceive all the importance of this generalization, 
when we come to speak of the satellites. 

(493. ) It will first, however, be proper to explain by what 



412 OUTLINES OF ASTRONOMY 

process of calculation the expression of a planet's elliptic 
orbit by its elements can be compared with observation, and 
how we can satisfy ourselves that the numerical data con- 
tained in a table of such elements for the whole system does 
really exhibit a true picture of it, and afford the means of 
determining its state at every instant of time, by the mere 
application of Kepler's laws. Now, for each planet, it is 
necessary for this purpose to know, 1st, the magnitude and 
form . of its ellipse ; 2dly, the situation of this ellipse in 
space, with respect to the ecliptic, and to a fixed line drawn 
therein ; 3dly, the local situation of the planet in its ellipse 
at some known epoch, and its periodic time or mean angular 
velocity, or, as it is called, its mean motion. 

(494.) The magnitude and form of an ellipse are deter- 
mined by its greatest length and least breadth, or its two 
principal axes; but for astronomical uses it is preferable to 
use the semi-axis major (or half the greatest length), and the 
excentricity or distance of the focus from the centre, which 
last is usually estimated in parts of the former. Thus, an 
ellipse, whose length is 10 and breadth 8 parts of any scale, 
has for its major semi- axis 5, and for its excentricity 3 such 
parts; but when estimated in parts of the semi-axis, regarded 
as a unit, the excentricity is expressed by the fraction -J. 

(495.) The ecliptic is the plane to which an inhabitant of 
the earth most naturally refers the rest of the solar system, 
as a sort of ground-plane ; and the axis of its orbit might be 
taken for a line of departure in that plane or origin of angu- 
lar reckoning. Were the axis fixed, this would be the best 
possible origin of longitudes ; but as it has a motion (though 
an excessively slow one), there is, in fact, no advantage in 
reckoning from the axis more than from the line of the equi- 
noxes, and astronomers therefore prefer the latter, taking 



'OUTLINES of astronomy 413 

account of its variation by the effect of precession, and re- 
storing it, by calculation at every instant, to a fixed position. 
Now, to determine the situation of the ellipse described by 
a planet with respect to this plane, three elements require to 
be known: — 1st, the inclination of the plane of the planet's 
orbit to the plane of the ecliptic; 2dly, the line in which 
these two planes intersect each other, which of necessity 
passes through the sun, and whose position with respect to 
the line of the equinoxes is therefore given by stating its 
longitude. This line is called the line of the nodes. When 
the planet is in this line, in the act of passing from the south 
to the north side of the ecliptic, it is in its ascending node, 
and its longitude at that moment is the element called the 
longitude of the node. These two data determine the situa- 
tion of the plane of the orbit; and there only remains for the 
complete determination of the situation of the planet's el- 
lipse, to know how it is placed in that plane, which (since 
its focus is necessarily in the sun) is ascertained by stating 
the longitude of its perihelion, or the place which the extrem- 
ity of the axis nearest the sun occupies, when orthographi- 
cally projected on the ecliptic. 8 

(496.) The- dimensions and situation of the planet's orbit 
thus determined, it only remains, for a complete acquaint- 
ance with its history, to determine the circumstances of its 
motion in the orbit so precisely fixed. Now, for this pur- 
pose, all that is needed is to know the moment of time when 
it is either at the perihelion, or at any other precisely deter- 
mined point of its orbit, and its whole period; for these 
being known, the law of the areas determines the place at 

6 What is most improperly called in some books the "longitude of the peri- 
helion on the orbit" is a broken arc or an angle made up of two in different 
planes, viz. from the equinox to the node on the ecliptic and thence to the 
perihelion on the orbit. 



414 OUTLINES OF ASTRONOMY 

every other instant. This moment is called (when the peri- 
helion is the point chosen) the perihelion passage, or, when 
some point of the orbit is fixed upon, without special refer- 
ence to the perihelion, the epoch. 

(497.) Thus, then, we have seven particulars or elements, 
which must be numerically stated, before we can reduce to 
calculation the state of the system at any given moment. 
But these known, it is easy to ascertain the apparent posi- 
tions of each planet, as it would be seen from the sun, or is 
seen from the earth at any time. The former is called the 
heliocentric, the latter the geocentric, place of the planet. 

(498.) To commence with the heliocentric places. Let S 
represent the sun; PAN the orbit of the planet, being an 
ellipse, having the S in its focus, and A for its perihelion; 
and let p a N T represent the projection of the orbit on the 
plane of the ecliptic, intersecting the line of equinoxes S T 
in T, which, therefore, is the origin of longitudes. Then 
will S N be the line of nodes; and if we suppose B to lie on 
the south, and A on the north side of the ecliptic, and the 
direction of the planet's motion to be 
from B to A, N will be the ascending 
^ node, and the angle T S N the longi- 
tude of the node. In like manner, if P 
be the place of the planet at any time, and if it and the 
perihelion A be projected on the ecliptic, upon the points 
p, a, the angles YSp, T S a, will be the respective helio- 
centric longitudes of the planet and of the perihelion, the 
former of which is to be determined, and the latter is one 
of the given elements. Lastly,, the angle p S P is the 
heliocentric latitude of the planet, which is also required 
to be known. 

(499.) Now, the time being given, and also the moment 




OUTLINES OF ASTRONOMY 415 

of the planet's passing the perihelion, the interval, or the 
time of describing the portion A P of the orbit, is given, 
and the periodical time, and the whole area of the ellipse 
being known, the law of proportionality of areas to the times 
of their description gives the magnitude of the area ASP. 
From this it is a problem of pure geometry to determine the 
corresponding angle ASP, which is called the planet's true 
anomaly. This problem is of the kind called transcenden- 
tal, and has been resolved by a great variety of processes, 
some more, some less intricate. It offers, however, no 
peculiar difficulty, and is practically resolved with great 
facility by the help of tables constructed for the purpose, 
adapted to the case of each particular planet. 7 

(500.) The true anomaly thus obtained, the planet's angu- 
lar distance from the node, or the angle N S P, is to be 
found. Now, the longitudes of the perihelion and node 
being respectively T a and T N, which are given, their dif- 
ference a N" is also given, and the angle N of the spherical 
right-angled triangle ANa, being the inclination of the plane 
of the orbit to the ecliptic, is known. Hence we calculate the 
arc N A, or the angle NSA, which, added to A S P, gives 
the angle NSP required. And from this, regarded as the 
measure of the arc N P, forming the hypothenuse of the 

7 It will readily be understood, that, except in the case of uniform circular 
motion, an equable description of areas about any centre is incompatible with 
an equable description of angles. The object of the problem in the text is to 
pass from the area, supposed known, to the angle, supposed unknown; in other 
words, to derive the true amount of angular motion from the perihelion, or the 
true anomaly from what is technically called the mean anomaly, that is, the 
mean angular motion which would have been performed had the motion in angle 
been uniform instead of the motion in area. It happens, fortunately, that this 
is the simplest of all problems of the transcendental kind, and can be resolved, 
in the most difficult case, by the rule of "false position," or trial and error, in 
a very few minutes. Nay, it may even be resolved approximately on inspection 
by a simple and easily constructed piece of mechanism, of which the reader may 
see a description in the Cambridge Philosophical Transactions, vol. iv. p. 425, by 
the author of this work. 



416 OUTLINES OF ASTRONOMY 

right-angled spherical triangle PN]), whose angle N, as be- 
fore, is known, it is easy to obtain the other two sides, N p 
and P p. The latter, being the measure of the angle j)SP, 
expresses the planet's heliocentric latitude; the former meas- 
ures the angle NS|), or the planet's distance in longitude 
from its node, which, added to the known angle T S N, the 
longitude of the node, gives the heliocentric longitude. 
This process, however circuitous it may appear, when once 
well understood may be gone through numerically by the 
aid of the usual logarithmic and trigonometrical tables, in 
little more time than it will have taken the reader to peruse 
its description. 

(501.) The geocentric differs from the heliocentric place 
of a planet by reason of that parallactic change of apparent 
situation which arises from the earth's motion in its orbit. 
Were the planets' distances as vast as those of the stars, the 
earth's orbital motion would be insensible when viewed from 
them, and they would always appear to us to hold the same 
relative situations among the fixed stars as if viewed from 
the sun, i.e. they would then be seen in their heliocentric 
places. The difference, then, between the heliocentric and 
geocentric places of a planet is, in fact, the same thing with 
its parallax, arising from the earth's removal from the cen- 
tre of the system and its annual motion. It follows from 
this, that the first step toward a knowledge of its amount, 
and the consequent determination of the apparent place of 
each planet, as referred from the earth to the sphere of the 
fixed stars, must be to ascertain the proportion of its linear 
distances from the earth and from the sun, as compared with 
the earth's distance from the sun, and the angular positions 
of all three with respect to each other. 

(502.) Suppose, therefore, S to represent the sun, E the 




OUTLINES OF ASTRONOMY 417 

earth, and P the planet; S Y the line of equinoxes, Y E 
the earth's orbit, and Ppa perpendicular let fall from the 
planet on the ecliptic. Then will the angle S P E (accord- 
ing to the general notion of parallax conveyed in art. 69) 
represent the parallax of the planet arising from the change 
of station from S to E ; E P will be the apparent direction 
of the planet seen from E ; and if S Q be drawn parallel to 
E p, the angle rSQ will be the geo- 
centric longitude of the planet, while 
rSE represents the heliocentric lon- 
gitude of the earth, Y S p that of 
the planet. The former of these, 
Y S E, is given by the solar tables; the latter, Y S p, is 
found by the process above described (art. 500). Moreover, 
S P is the radius vector of the planet's orbit, and S E that 
of the earth's, both of which are determined from the known 
dimensions of their respective ellipses, and the places of the 
bodies in them at the assigned time. Lastly, the angle 
P Sp is the planet's heliocentric latitude. 

(503.) Our object, then, is, from all these data, to deter- 
mine the angle rSQ, and PEp, which is the geocentric 
latitude. The process, then, will stand as follows: — 1st, 
In the triangle S P p, right-angled at p, given S P, and 
the angle P S p (the planet's radius vector and helio- 
centric latitude), find S p and P p; 2dly, In the triangle 
SE|), given S p (just found), S E (the earth's radius vec- 
tor), and the angle E S p (the difference of heliocentric 
longitudes of the earth and planet), find the angle S p E, 
and the side E p. The former being equal to the alternate 
angle p S Q, is the parallactic removal of the planet in 
longitude, which, added to Y S p, gives its geocentric 
longitude. The latter, E p (which is called the curtate dis» 



418 OUTLINES OF ASTRONOMY 

tance of the planet from the earth), gives at once the geo- 
centric latitude, by means of the right-angled triangle PEp, 
of which E p and P p are known sides, and the angle 
P E p is the geocentric latitude sought. 

(504.) The calculations required for these purposes are 
nothing but the most ordinary processes of plane trigonom- 
etry; and, though somewhat tedious, are neither intricate 
nor difficult. When executed, however, they afford us the 
means of comparing the places of the planets actually ob- 
served with the elliptic theory, with the utmost exactness, 
and thus putting it to the severest trial; and it is upon the 
testimony of such computations, so brought into comparison 
with observed facts, that we declare that theory to be a true 
representation of nature. 

(505.) The planets Mercury, Venus, Mars, Jupiter and 
Saturn have been known from the earliest ages in which 
astronomy has been cultivated. Uranus was discovered by 
Sir W. Herschel in 1781, March 13th, in the course of 
a review of the heavens, in which every star visible in a 
telescope of a certain power was brought under close 
examination, when the new planet was immediately de- 
tected by its disk, under a high magnifying power. It has 
since been ascertained to have been observed on many 
previous occasions, with telescopes of insufficient power to 
show its disk, and even entered in catalogues as a star; and 
some of the observations which have been so recorded have 
been used to improve and extend our knowledge of its 
orbit. The discovery of the asteroids dates from the first 
day of 1801, when Ceres was discovered by Piazzi, at 
Palermo, a discovery speedily followed by those of Juno 
by Professor Harding, of Gottingen, in 1804; and of Pallas 
and Yesta, by Dr. Olbers, of Bremen, in 1802 and 1807 re- 



OUTLINES OF ASTRONOMY 419 

spectively. It is extremely remarkable that this important 
addition to our system had been in some sort surmised as 
a thing not unlikely, on the ground that the intervals be- 
tween the orbit of Mercury and the other planetary orbits, 
go on doubling as we recede from the sun, or nearly so. 
Thus, the interval between the orbits of the Earth and 
Mercury is nearly twice that between those of Venus and 
Mercury; that between the orbits of Mars and Mercury 
nearly twice that between the Earth and Mercury; and so 
on. The interval between the orbits of Jupiter and Mer- 
cury, however, is much too great, and would form an ex- 
ception to this law, which is, however, again resumed in 
the case of the three planets next in order of remoteness, 
Jupiter, Saturn, and Uranus. It was therefore thrown out, 
by the late Professor Bode, of Berlin, 8 as a possible surmise, 
that a planet not then yet discovered might exist between 
Mars and Jupiter; and it may easily be imagined what was 
the astonishment of astronomers on finding not one only, 
but four planets, differing greatly in all the other elements 
of their orbits, but agreeing very nearly, both inter se, and 
with the above stated empirical law, in respect of their mean 
distances from the sun. No account, d priori or from theory, 

8 The progression is (rather rudely) that of the numbers 4, 4 4- 3, 4 -f- 6, 
4-4-12, etc. The empirical law itself, as we have above stated it, is ascribed 
by Voiron, not to Bode (who would appear, however, at all events, to have 
first drawn attention to this interpretation of its interruption), but to Professor 
Titius of Wittemberg. (Voiron, Supplement to Bailly.) 

Another law has been proposed (in a letter to the writer, dated March 
1, 1869), by Mr. J. Jones, of Brynhyfryd, Wrexham. If the planets' mean 
distances from the sun be arranged in the following orders. — Mercury, Venus, 
Jupiter, Saturn; — the Earth, Mars, Uranus, Neptune; — the product of the 
means in each group is nearly equal to the product of the extremes. 
Venus x Jupiter Earth x Neptune , T .,-,,„ ^ , , 

— ^-t — = t? =r = 1. In pomt of fact the first fraction 

Mercury x Saturn Mars x Uranus 

«=1'02; and the last = zr-^-r, so that the approach to verification of the law 

is really very near. 



420 OUTLINES OF ASTRONOMY 

was to be given of this singular progression, which is not, 
like Kepler's laws, strictly exact in numerical verification: 
but the circumstances we have just mentioned tended to 
create a strong belief that it was something beyond a mere 
accidental coincidence, and bore reference to the essential 
structure of the planetary system. It was even conjectured 
that the asteroids are fragments of some greater planet 
which formerly circulated in that interval, but which has 
been blown to atoms by an explosion; an idea countenanced 
by the exceeding minuteness of these bodies which present 
disks ; and it was argued that in that case innumerable more 
such fragments must exist and might come to be hereafter 
discovered. Whatever may be thought of such a specula- 
tion as a physical hypothesis, this conclusion has been 
verified to a considerable extent as a matter of, fact by sub- 
sequent discovery, the result of a careful and minute ex- 
amination and mapping down of the smaller stars in and 
near the zodiac, undertaken with that express object. 
Zodiacal charts of this kind, the product of the zeal and 
industry of many astronomers, have been constructed, in 
which every star down to the ninth, tenth, or even lower 
magnitudes, is inserted, and these stars being compared 
with the actual stars of the heavens, the intrusion of any 
stranger within their limits cannot fail to be noticed when 
the comparison is systematically conducted. The discovery 
of Astrsea and Hebe by Professor Hencke in 1845 and 1847 
revived the flagging spirit of inquiry in this direction; with 
what success, the list in the Appendix to this volume will 
best show. The labors of our indefatigable countryman, 
Mr. Hind, have been rewarded by the discovery of no less 
than eight of them. 

(506.) The discovery of Neptune marks in a signal man- 



OUTLINES OF ASTRONOMY 421 

ner the maturity of Astronomical science. The proof, or 
at least the urgent presumption of the existence of such 
a planet, as a means of accounting (by its attraction) for 
certain small irregularities observed in the motions of 
Uranus, was afforded almost simultaneously by the inde- 
pendent researches of two geometers, Messrs. Adams of 
Cambridge and Leverrier of Paris, who were enabled, from 
theory alone, to calculate whereabout it ought to appear in 
the heavens, if visible, the places thus independently calcu- 
lated agreeing surprisingly. Within a single degree of the 
place assigned by M. Leverrier' s calculations, and by him 
communicated to Dr. Gralle of the Royal Observatory at 
Berlin, and within two and a half from that indicated by 
Mr. Adams, it was actually found by Dr. Gralle on the very 
first night (Sept. 23, 1846) after the receipt of M. Leverrier 's 
communication, on turning a telescope on the spot, and 
comparing the stars in its immediate neighborhood with 
those previously laid down in one of the zodiacal charts 
already alluded to. 9 

(507.) The mean distance of Neptune from the sun, how- 
ever, so far from falling in with the supposed law of plan- 
etary distances above mentioned, offers a decided case 
of discordance. The interval between its orbit and that 
of Mercury, instead of being nearly double the interval 

9 Constructed by Dr. Bremiker, of Berlin. On reading the history of this 
noble discovery, we are ready to exclaim with Schiller — 

"Mit dem Genius steht die Natur im ewigem Bunde, 
Was der Eine verspricht leistet die Andre gewiss." 

Professor Challis, of the Cambridge Observatory, directing the Northumber- 
land telescope of that Institution to the place assigned by Mr. Adams's calcula- 
tions and its vicinity, on the 4th and 12th of August, 1846, saw the planet on 
both those days, and noted its place (among those of other stars) for re-observa- 
tion. He, however, postponed the comparison of the places observed, and not 
possessing Dr. Bremiker's chart (which would have at once indicated the pres- 
ence of an unmapped star), remained in ignorance of the planet's existence as 
a visible object till its announcement as such by Dr. Galle, 



422 OUTLINES OF ASTRONOMY 

between those of Uranus and Mercury, does not, in fact, 
exceed the latter interval by much more than half its 
amount. This remarkable exception may serve to make 
us cautious in the too ready admission of empirical laws 
of this nature to the rank of fundamental truths, though, as 
in the present instance, they may prove useful auxiliaries, 
and serve as stepping stones, affording a temporary footing 
in the path to great discoveries. The force of this remark 
will be more apparent when we come to explain more par- 
ticularly the nature of the theoretical views which led to 
the discovery of Neptune itself. 

(508.) We shall devote the rest of this chapter to an ac- 
count of the physical peculiarities and probable condition 
of the several planets, so far as the former are known by 
observation, or the latter rest on probable grounds of con- 
jecture. In this, three features principally strike us as 
necessarily productive of extraordinary diversity in the 
provisions by which, if they be, like our earth, inhabited, 
animal life must be supported. These are, first, the differ- 
ence in their respective supplies of light and heat from the 
sun; secondly, the difference in the intensities of the gravi- 
tating forces which must subsist at their surfaces, or the 
different ratios which, on their several globes, the inertice 
of bodies must bear to their weights; and, thirdly, the 
difference in the nature of the materials of which, from 
what we know of their mean density, we have every reason 
to believe they consist. The intensity of solar radiation is 
nearly seven times greater on Mercury than on the Earth, 
and on Neptune 900 times less; the proportion between the 
two extremes being that of upward of 5600 to 1. Let any 
one figure to himself the condition of our globe, were the 
sun to be septupled, to say nothing of the greater ratio! or 



OUTLINES OF ASTRONOMY 423 

were it diminished to a seventh, or to a 900th of its actual 
power ! It is true that owing to the remarkable difference 
between the properties of radiant heat as emitted from 
bodies of very exalted temperature, as the sun, and as 
from such as we commonly term ivarm, it is very possible 
that a dense atmosphere surrounding a planet, while allow- 
ing the access of solar heat to its surface, may oppose a 
powerful obstacle to its escape, and that thus the feeble 
sunshine on a remote planet may be retained and accumu- 
lated on its surface in the same way (and for the same 
reason) that a very slight amount of sunshine, or even the 
dispersed heat of a bright though clouded day, suffices to 
maintain the interior of a closed greenhouse at a high 
temperature. VTe cannot then absolutely conclude the 
prevalence of that excessive cold on the surface of a dis- 
tant planet which its mere remoteness from the sun might 
lead us, prima facie, to expect. 

(508 b.) Again, the intensity of gravity, or its efficacy in 
counteracting muscular power and repressing animal activ- 
ity, on Jupiter, is nearly two and a half times that on the 
Earth, on Mars not more than one- half, on the Moon one- 
sixth, and on the smaller planets probably not more than 
one -twentieth: giving a scale of which the extremes are in 
the proportion of sixty to one. Lastly, the density of Sat- 
urn hardly exceeds one- eighth of the Earth's, so that it 
must consist of materials not heavier on the average than 
dry fir wood. Now, under the various combinations of ele- 
ments so important to life as these, what immense diversity 
must we not admit in the conditions of that great problem, 
the maintenance of animal and intellectual existence and 
happiness, which seems, so far as we can judge by what we 
see around us in our own planet, and by the way in which 



424 OUTLINES OF ASTRONOMY 

every corner of it is crowded with living beings, to form an 
unceasing and worthy object for the exercise of the Benevo- 
lence and Wisdom which preside over all ! 

(509.) Quitting, however, the region of mere speculation, 
we will now show what information the telescope affords us 
of the actual condition of the several planets within its reach. 
Of Mercury we can see little more than that it is round, and 
exhibits phases. It is too small, and too much lost in the 
constant neighborhood of the Sun, to allow us to make out 
more of its nature. The real diameter of Mercury is about 
3200 miles : its apparent diameter varies from 5" to 12". Nor 
does Yenus offer any remarkable peculiarities: although its 
real diameter is 7800 miles, and although it occasionally at- 
tains the considerable apparent diameter of 61/, which is 
larger than that of any other planet, it is yet the most diffi- 
cult of them all to define with telescopes. The intense lus- 
tre of its illuminated part dazzles the sight, and exaggerates 
every imperfection of the telescope; yet we see clearly that 
its surface is not mottled over with permanent spots like the 
Moon; we notice in it neither mountains nor shadows, but a 
uniform brightness, in which sometimes we may indeed 
fancy, or perhaps more than fancy, brighter or obscurer 
portions, but can seldom or never rest fully satisfied of the 
fact. It is from some observations of this kind that both 
Venus and Mercury have been concluded to revolve on their 
axes in about the same time as the Earth, though in the case 
of Yenus, Bianchini and other more recent observers have 
contended for a period of twenty-four times that length. 
The most natural conclusion, from the very rare appearance 
and want of permanence in the spots, is, that we do not see, 
as in the Moon, the real surface of these planets, but only 
their atmospheres, much loaded with clouds, and which may 



OUTLINES OF ASTRONOMY 425 

serve to mitigate the otherwise intense glare of their sun- 
shine. 

(510.) The case is very different with Mars. In this 
planet we frequently discern, with perfect distinctness, the 
outlines of what may be continents and seas. (See Plate III. 
fig. 1, which represents Mars in its gibbous state, as seen on 
the 16th of August, 1830, in the 20-feet reflector at Slough.) 
Of these, the former are distinguished by that ruddy color 
which characterizes the light of this planet (which always 
appears red and fiery), and indicates, no doubt, an ochrey 
tinge in the general soil, like what the red sandstone dis- 
tricts on the Earth may possibly offer to the inhabitants of 
Mars, only more decided. Contrasted with this (by a gen- 
eral law in optics), the seas, as we may call them, appear 
greenish. 10 These spots, however, are not always to be seen 
equally distinct, but, when seen, they offer the appearance 
of forms considerably definite and highly characteristic, 11 
brought successively into view by the rotation of the 
planet, from the assiduous observation of which it has even 
been found practicable to construct a rude chart of the sur- 
face of the planet. The variety in the spots may arise from 
the planet not being destitute of atmosphere and clouds; 
and what adds greatly to the probability of this is the ap- 
pearance of brilliant white spots at its poles — one of which 
appears in our figure — which have been conjectured, with 
some probability, to be snow ; as they disappear when they 
have been long exposed to the sun, and are greatest when 



10 I have noticed the phenomena described in the text on many occasions, 
but never more distinct than on the occasion when the drawing was made from 
which the figure in Plate I. is engraved. — Author. 

11 The reader will find many of those forms represented in Schumacher's 
Astronomische Nachrichten, No. 191, 434, and in the chart in No. 349, by 
Messrs. Beer and Madler. 



426 . OUTLINES OF ASTRONOMY 

just emerging from the long night of their polar winter, the 
snow line then extending to about six degrees (reckoned on 
a meridian of the planet) from the pole. By watching the 
spots during a whole night, and on successive nights, it is 
found that Mars has a rotation on an axis inclined about 
30° 18' to the ecliptic, and in a period of 24 h 37 m 23 s ia in the 
same direction as the Earth's, or from west to east. The 
greatest and least apparent diameters of Mars are 4" and 18', 
and its real diameter about 4100 miles. 

(511.) We now come to a much more magnificent planet, 
Jupiter, the largest of them all, being in diameter no less 
than 87,000 miles, and in bulk exceeding that of the Earth 
nearly 1300 times. It is, moreover, dignified by the attend- 
ance of four moons, satellites, or secondary planets, as they 
are called, which constantly accompany and revolve about 
it, as the Moon does round the Earth, and in the same direc- 
tion, forming with their principal, or primary, a beautiful 
miniature system, entirely analogous to that greater one of 
which their central body is itself a member, obeying the 
same laws, and exemplifying, in the most striking and in- 
structive manner, the prevalence of the gravitating power as 
the ruling principle of their motions: of these, however, wo 
shall speak more at large in the next chapter. 

(512.) The disk of Jupiter is always observed to be 
crossed in one certain direction by dark bends or belts 
presenting the appearance, in Plate III. Jig. 2, which rep- 
resents this planet as seen on the 23d of September, 1832, in 
the 20-feet reflector at Slough. These belts are, however, 
by no means alike at all times ; they vary in breadth and in 
situation on the disk (though never in their general direc- 

13 Beer and Madler, Astr. Nachr. 349. 22«-f36, Proctor, A. S. Not. xxix. 232. 



OUTLINES OF ASTRONOMY 427 

tion). They have even been seen broken up and distributed 
over the whole face of the planet; but this phenomenon is 
extremely rare. Branches running out from them, and sub- 
divisions, as represented in the figure, as well as evident 
darker spots, are by no means uncommon. But the most 
singular phenomenon presented by the belts of Jupiter is 
the occasional appearance upon them of perfectly round, 
well defined, bright spots, not unlike the disks of the satel- 
lites (see art. 540), as they are occasionally seen projected 
on the planet when passing between it and the Earth, only 
smaller. They vary in situation and number, as many as 
ten having, on one occasion (Oct. 28, 1857), been seen at 
once, "but, so far as hitherto observed, only on the southern 
hemisphere of Jupiter. They were first noticed by Mr. 
Dawes in the spring of 1849, but first described and figured 
by Mr. Lassell, March 27, 1850. They have been more re- 
cently again and more distinctly and consecutively observed 
by the former of these observers, who has given figures of 
them in Ast. Soc. Not. xviii. pp. 8, 40. 

(512 a.) From the appearances and configurations of the 
belts, attentively watched, it is concluded that this planet 
revolves in the surprisingly short period of 9 h 55 m 21 8, 3 
(Airy), on an axis perpendicular to the direction of the 
belts. Now, it is very remarkable, and forms a most satis- 
factory comment on the reasoning by which the spheroidal 
figure of the Earth has been deduced from its diurnal rota- 
tion, that the outline of Jupiter's disk is evidently not cir- 
cular, but elliptic, being considerably flattened in the direc- 
tion of its axis of rotation. This appearance is no optical 
illusion, but is authenticated by micrometrical measures, 
which assign 106 to 100 for the proportion of the equatorial 
and polar diameters. And to confirm, in the strongest man- 



428 OUTLINES OF ASTRONOMY 

ner, the truth of those principles on which our former con 
elusions have been founded, and fully to authorize their ex 
tension to this remote system, it appears, on calculation 
that this is really the degree of oblateness which corre 
sponds, on those principles, to the dimensions of Jupiter 
and to the time of his rotation. 

(513.) The parallelism of the belts to the equator of 
Jupiter, their occasional variations, and these appearances 
of spots seen upon them, render it extremely probable that 
they subsist in the atmosphere of the planet, forming tracts 
of comparatively clear sky, determined by currents analo- 
gous to our trade- winds, but of a much more steady and 
decided character, as might indeed be expected from the 
immense velocity of its rotation. That it is the compara- 
tively darker body of the planet which appears in the belts 
is evident from this — that they do not come up in all their 
strength to the edge of the disk, but fade away gradually 
before they reach it. The round bright spots described 
above may therefore not impossibly be insulated masses 
of cloud, of local origin, analogous to the cumuli which 
sometimes cap ascending columns of vapor in our atmo- 
sphere. The apparent diameter of Jupiter varies from 30" 
to 46V 3 

(514.) A still more wonderful, and, as it may be termed, 
elaborately artificial mechanism, is displayed in Saturn, the 
next in order of remoteness to Jupiter, to which it is not 
much inferior in magnitude, being about 79,000 miles in 
diameter, nearly 1000 times exceeding the earth in bulk, and 
subtending an apparent angular diameter at the earth, of 



13 Prof. P„ Smyth and Mr. De la Rue have published fine representations of 
Jupiter, the former as seen from the Peak of Teneriffe (alt 10, TOO ft.), the latter 
in his observatory at Cranford. 



OUTLINES OF ASTRONOMY 429 

about 18" at its mean distance. This stupendous globe, 
besides being attended by no less than eight satellites, or 
moons, is surrounded with three broad, flat, and extremely 
thin rings, concentric with the planet and with each other, 
the inner being very faint and semi-transparent; all lying in 
one plane, and separated by a very narrow interval from 
each other throughout their whole circumference, as they 
are from the planet by a much wider. The dimensions of 
this extraordinary appendage are as follows: — 14 



Exterior diameter of exterior bright ring . 

Interior ditto 

Exterior diameter of interior bright ring . 
Interior ditto .... 

Equatorial diameter of the body 
Interval between the planet and interior bright ring 
Interval of the rings ..... 
Thickness of the ring not exceeding 



" Miles 

40-095 = 176,418 

35-289 = 155,272 

34-475 = 151,690 

26-668 = 117,339 

17-991= 79,160 

4-339= 19,090 

0-408= 1,791 

= 250 



The figure (Plate III. fig. 3) represents Saturn surrounded 
by its rings, and having its body striped with dark belts, 
somewhat similar, but broader and less strongly marked than 
those of Jupiter, and owing, doubtless, to a similar cause. 16 
Whatever be the materials of which the ring consists (and 
there are strong reasons, art. 522, for believing it not to 
consist of solid matter), it is at least substantial enough to 
cast a shadow, which, when the Earth is properly situated, 
may be seen on the body of the planet on the side next the 
Sun; as also to receive one when thrown on it by the body 



14 These dimensions are calculated from Prof. Struve's micrometric meas- 
ures, Mem. Ast. Soc. iii. 301, with the exception of the thickness of the ring, 
which is concluded from its total disappearance in 1833, in a telescope which 
would certainly have shown, as a visible object, a line of light one-twentieth 
of a second in breadth. The interval of the rings here stated is possibly some- 
what too small. 

15 The equatorial bright belt is generally well seen. The subdivision of the 
dark one by two narrow bright bands is seldom so distinct as represented in 
the plate. 



430 OUTLINES OF ASTRONOMY 

on the opposite side. The form of this latter shadow, mi- 
nutely scrutinized with powerful telescopes, has led some 
observers to conclude that the edge of the outer ring is in 
some degree rounded, aDd that the two rings do not lie pre- 
cisely in one plane. 16 From the parallelism of the belts 
with the plane of the ring, it may be conjectured that the 
axis of rotation of the planet is perpendicular to that plane; 
and this conjecture is confirmed by the occasional appear- 
ance of extensive dusky spots on its surface, which, when 
watched, like the spots on Mars or Jupiter, indicate a rota- 
tion in 10 h 16 m 9, 44 (according to the observations of Sir 
Wm. Herschel) about an axis so situated. 

(515.) The axis of rotation, like that of the earth, pre- 
serves its parallelism to itself during the motion of the 
planet in its orbit; and the same is also the case with 
the ring, whose plane is constantly inclined at the same, 
or very nearly the same, angle to that of the orbit, and, 
therefore, to the ecliptic, viz. 28° 11'; and intersects the 
latter plane in a line, which makes at present" an angle 
with the line of equinoxes of 167° 31'. So that the nodes of 
the ring lie in 167° 31' and 347° 31' of longitude. Whenever, 
then, the planet happens to be situated in one or other of 
these longitudes, as at C, the plane of the ring passes 
through the sun, which then illuminates only the edge of 
it. And if the earth at that moment be in F, it will see 
the ring edgewise, the planet being in opposition, and 
therefore most favorably situated (cceteris paribus) for ob- 



16 The excessive thinness of the rings leads us to demur to the former of 
these conclusions as a result of observation, though fully admitting it as theo- 
retically probable. 

17 According to Bessel, the longitude of the node of the ring increases by 
46" -462 per annum. In 1800 it was 166° 53' 8" '9. 



OUTLINES OF ASTRONOMY 



481 



servation. Under these circumstances the ring, if seen at 
all, can only appear as a very narrow straight line of light 
projecting on either side of the body as a prolongation of 
its diameter. In fact, it is quite invisible in any but tel- 
escopes of extraordinary power. 18 This remarkable phe- 
nomenon takes place at intervals of fifteen years nearly 
(being a semi-period of Saturn in its orbit). One disap- 
pearance at least must take place whenever Saturn passes 
either node of its orbit; but three must frequently happen, 
and two are possible. To show this, suppose S to be the 




sun, A B C D part of Saturn's orbit situated so as to in- 
clude the node of the ring (at C); E F Gr H the Earth's 
orbit; S the line of the node; EB,GD parallel to S 
touching the Earth's orbit in E G-; and let the direction 
of motion of both bodies be that indicated by the arrow. 
Then since the ring preserves its parallelism, its plane can 
nowhere intersect the Earth's orbit, and therefore no disap- 
pearance can take place, unless the planet be between B and 



18 Its disappearance was complete when observed with a reflector eighteen 
inches in aperture and twenty feet in focal length on the 29 th of April, 1833, 
by the author, 



432 OUTLINES OF ASTRONOMY 

D: and, on the other hand, a disappearance is possible (if 
the Earth be rightly situated) during the whole time of the 
description of the arc B D. Now, since S B or S D, the 
distance of Saturn from the Sun, is to S E or S G, that of 
the Earth, as 9-54 to 1, the angle C S Dor C S B=6°l', 
and the whole angle B S D=12° 2', which is described by 
Saturn (on an average) in 359 -46 days, wanting only 5 -8 days 
of a complete year. The Earth then describes very nearly 
an entire revolution within the limits of time when a disap- 
pearance is possible; and since, in either half of its orbit 
E F G or G H E, it may equally encounter the plane of the 
ring, one such encounter at least is unavoidable within 
the time specified. 

(516.) Let G a be the arc of the Earth's orbit described 
from G in 5*8 days. Then if, at the moment of Saturn's 
arrival at B, the Earth be at a, it will encounter the plane 
of the ring advancing parallel to itself and to B E to meet 
it, somewhere in the quadrant H E, as at M, after which it 
will be behind that plane (with reference to the direction 
of Saturn's motion) through all the "arc M E F G up to G, 
where it will again overtake it at the very moment of the 
planet quitting the arc B D. In this state of things there 
will be two disappearances. If, when Saturn is at B, the 
Earth be anywhere in the arc a H E, it is equally evident 
that it will meet and pass through the advancing plane of 
the ring somewhere in the quadrant H E, that it will again 
overtake and pass through it somewhere in the semicircle 
E F G, and again meet it in some point of the quadrant 
G H, so that three disappearances will take place. So, also, 
if the Earth be at E when Saturn is at B, the motion of the 
Earth being at that instant directly toward B, the plane of 
the ring will for a short time leave it behind; but the ground 



OUTLINES OF ASTRONOMY 433 

so lost being rapidly regained, as the Earth's motion becomes 
oblique to the line of junction, it will soon overtake and 
pass through the plane in the early part of the quadrant 
E F, and passing on through G before Saturn arrives at D, 
will meet the plane again in the quadrant Gr H. The same 
will continue up to a certain point 5, at which, if the Earth 
be initially situated, there will be but two disappearances — 
the plane of the ring there overtaking the Earth for an in- 
stant, and being immediately again left behind by it, to be 
again encountered by it in G H. Finally, if the initial place 
of the Earth (when Saturn is at B) be in the arc b F a, there 
will be but one passage through the plane of the ring, viz. 
in the semicircle Gr H E, the Earth being in advance of that 
plane throughout the whole of b G. 

(517.) The appearances will moreover be varied according 
as the Earth passes from the enlightened to the unenlight- 
ened side of the ring, or vice versd. If C be the ascending 
node of the ring, and if the under side of the paper be sup- 
posed south and the upper north of the ecliptic, then, when 
the Earth meets the plane of the ring in the quadrant H E, 
it passes from the bright to the dark side: where it overtakes 
it in the quadrant E F, the contrary. Vice versa, when it 
overtakes it in F G, the transition is from the bright to the 
dark side, and the contrary where it meets it in G H. On 
the other hand when the Earth is overtaken by the ring- 
plane in the interval E 5, the change is from the bright to 
the dark side. When the dark side is exposed to sight, the 
aspect of the planet is very singular. It appears as a bright 
round disk, with its belts, etc. , but crossed equatorially by 
a narrow and perfectly black line. This can never of course 
happen when the planet is more than 6° 1' from the node of 

the ring. Generally, the northern side is enlightened and 
Astronomy— Vol XIX.— 19 



434 OUTLINES OF ASTRONOMY 

visible when the heliocentric longitude of Saturn is between 
173° 32' and 341° 30', and the southern when between 353° 
32' and 161° 30'. The greatest opening of the ring occurs 
when the planet is situated at 90° distance from the node 
of the ring, or in longitudes 77° 31' and 257° 31', and at 
these points the longer diameter of its apparent ellipse is 
almost exactly double the shorter. 

(518.) It will naturally be asked how so stupendous an 
arch, if composed of solid and ponderous materials, can be 
sustained without collapsing and falling in upon the planet? 
The answer to this is to be found in a swift rotation of the 
ring in its own plane, which observation has detected, owing 
to some portion of the ring being a little less bright than 
others, and assigned its period at 10 h 32 m 15 = , which, from 
what we know of its dimensions, and of the force of gravity 
in the Saturnian system, is very nearly the periodic time of 
a satellite revolving at the same distance as the middle of its 
breadth. It is the centrifugal force, then, arising from this 
rotation, which sustains it; and although no observations 
nice enough to exhibit a difference of periods between the 
outer and inner rings have hitherto been made, it is more 
than probable that such a difference does subsist as to place 
each independently of the other in a similar state of equilib- 
rium. Still, it might be urged, such is the thinness of the 
rings that it may very well be doubted, whether the strain 
brought upon either of them by the difference of its interior 
and exterior centrifugal forces, if solid, would not suffice to 
tear it in pieces. A fluid constitution would obviate this 
difficulty; and indeed it is very possible that the rings may 
be gaseous, or rather such a mixture of gas and vapor as 
consists with our idea of a cloud. 

(519 ) Although the rings are, as we hrve said, very 



OUTLINES OF ASTRONOMY 435 

nearly concentric with the body of Saturn, yet micromet- 
rical measurements of extreme delicacy 19 have demonstrated 
that the coincidence is not mathematically exact, but that 
the centre of gravity of the rings oscillates round that of 
the body, describing a very minute orbit, probably under 
laws of much complexity. Trifling as this remark may 
appear, it is of the utmost importance to the stability of 
the system of the rings, if solid and coherent. Supposing 
them mathematically perfect in their circular form, and 
exactly concentric with the planet, it is demonstrable that 
they would form a system in a state of unstable equilibrium, 
which the slightest external power would subvert — not by 
causing a rupture in the substance of the rings — but by pre- 
cipitating them unbroken on the surface of the planet. For 
the attraction of such a ring or rings on a point or sphere 
excentrically within them, is not the same in all directions, 
but tends to draw the point or sphere toward the nearest 
part of the ring, or away from the centre. Hence, sup- 
posing the body to become, from any cause, ever so little 
excentric to the ring, the tendency of their mutual gravity 
is not to correct but to increase this excentricity, and to 
bring the nearest parts of them together. Now, external 
powers, capable of producing such excentricity, exist in the 
attractions of the satellites, as will be shown in Chapter 
XII. ; and in order that the system may be stable, and 
possess within itself a power of resisting the first inroads 
of such a tendency, while yet nascent and feeble, and op- 
posing them by an opposite or maintaining power, it has 
been shown that it is sufficient to admit the rings, if solid, 



19 By Struve, confirming a suspicion suggested by the eye-observations 
of M. Schwabe. 



436 OUTLINES OF ASTRONOMY 

to be haded in some part of their circumference, either by 
some minute inequality of thickness, or by some portions 
being denser than others. Such a load would give to the 
whole ring to which it was attached somewhat of the char- 
acter of a heavy and sluggish satellite maintaining itself in 
an orbit with a certain energy sufficient to overcome minute 
causes of disturbance, and establish an average bearing on 
its centre. But even without supposing the existence of any 
such load — of which, after all, we have no proof — and grant- 
ing, in its full extent, the general instability of the equilib- 
rium, we think we perceive, in the rapid periodicity of all 
the causes of disturbance, a sufficient guarantee of its preser- 
vation. However homely be the illustration, we can con- 
ceive nothing more apt, in every way, to give a general 
conception of this maintenance of equilibrium under a con- 
stant tendency to subversion, than the mode in which a 
practiced hand will sustain a long pole in a perpendicular 
position resting on the finger, by a continual and almost 
imperceptible variation of the point of support. Be that, 
however, as it may, the observed oscillation of the centres 
of the rings about that of the planet is in itself the evidence 
of a perpetual contest between conservative and destructive 
powers — both extremely feeble, but so antagonizing one 
another as to prevent the latter from ever acquiring an 
uncontrollable ascendency, and rushing to a catastrophe. 

(520.) This is also the place to observe, that as the 
smallest difference of velocity between the body and the 
rings must infallibly precipitate the latter on the former, 
never more to separate (for they would, once in contact, 
have attained a position of stable equilibrium, and be held 
together ever after by an immense force) ; it follows, either 
that their motions in their common orbit round the sun must 



OUTLINES OF ASTRONOMY 437 

have been adjusted to each other by an external power, with 
the minutest precision, or that the rings must have been 
formed about the planet while subject to their common orbi- 
tal motion, and under the full and free influence of all the 
acting forces. 

(521.) [The exterior ring of Saturn is described by many 
observers as rather less luminous than the interior, .and the 
inner portion of this latter than its outer. On the night of 
November 11, 1850, however, Mr. G. B. Bond, of the Har- 
vard Observatory (Cambridge, U. S.), using the great Fraun- 
hofer equatorial of that institution, became aware of a line 
of demarcation between these two portions so definite, and 
an extension inward of the dusky border to such an extent 
(one- fifth, by measurement, of the joint breadth of the two 
old rings), as to justify him in considering it as a newly-dis- 
covered ring. On the nights of the 25th and 29th of the 
same month, and without knowledge of Mr. Bond's obser- 
vations, Mr. Dawes, at his observatory at Wateringbury, by 
the aid of an exquisite achromatic by Merz, of 6J- inches 
aperture, observed the very same fact, and even more dis- 
tinctly, so as to be sure of a decidedly darker interval be- 
tween the old and new rings, and even to subdivide the 
latter into two of unequal degrees of obscurity, separated 
by a line more obscure than either. 

(522.) Dr. Galle of Berlin, however, would appear to 
have been the first to notice (June 10, 1838) a faint exten- 
sion of the inner ring toward the body of the planet, to 
about half the interval between' the then recognized inner 
ring and the body, as shown by micrometrical measures. But 
this result remained unpublished (or at least not generally 
known) until after the observations of Messrs. Bond and 
Dawes. The most remarkable feature of this singular dis- 



438 OUTLINES OF ASTRONOMY 

covery is, that subsequent observations, from many quar 
ters, have concurred in showing the new ring to consist of 
semi-transparent materials through which the limb of the planet 
may be seen up to the edge of the interior bright ring. Dark 
lines (apparently of a transitory nature) have been observed 
on the bright rings parallel to the permanent dark interval 
dividing them. All these indications taken in conjunction 
with what is said in art. 518 decidedly point to a vaporous 
constitution of these wonderful appendages. 20 ] 

(522 a.) Still it has been thought remarkable that this 
new ring, or appendage to the rings, should not have been 
discovered earlier; and it has even been conjectured that 
the breadth of the ring has been gradually increasing inward 
since the time of Huyghens, its first discoverer: and this 
conjecture for a while appeared to be supported by micro- 
metrical measures obtained by M. Otto Struve (with whom 
the conjecture originated), which seemed to show a still fur- 
ther diminution of the interval between the rings and the 
ball. The question, however, appears to be definitively 
settled in the negative by the elaborate micrometrical meas- 
ures of Mr. Main, at the Koyal Observatory at Greenwich, 21 
and by the discussions entered into by M. Kaiser. 22 

(522 b.) The rings of Saturn must present a magnificent 
spectacle from those regions of the planet which lie above 
their enlightened sides, being seen as vast luminous arches, 
spanning the sky from horizon to horizon, and holding an 



20 The passage of Saturn across any considerable star would afford an admir- 
able opportuDity of testing the existence of fissures in the rings, as it would 
flash in succession through them. The opportunity of watching for such oc- 
cupations— when Saturn traverses the Milky Way, for instance — should not 
be neglected. 

21 Mem. Ast. Soc. xxv. 

22 Ast. Soc. Notice, xvi. 66. 



OUTLINES OF ASTRONOMY 



439 



almost invariable situation among the stars. To a spectator 
situated anywhere in the axis of the planet, it is evident 
that their interior and exterior outlines must both appear as 
circles corresponding to parallels of declination, and must 
occasion a permanent eclipse of every heavenly body lying 
between these parallels. It is otherwise to a spectator situ- 
ated on the planet's surface. To such a one the interior and 
exterior outline of each ring would, by the effect of per- 
spective, be thrown into nonconcentric ellipses, so that (sup- 
posing he could see through the whole planet and obtain a 
view of the whole ring) it would appear broader on the side 



,.--a 




nearest to him than on that most remote. These ellipses, 
moreover, when traced along the heavens, would not coin- 
cide with parallels of declination; 33 but would deviate from 
such parallels toward the elevated pole, as is evident, if we 
consider that a perpendicular S T from any point S on the 
planet's surface to the plane of the ring A B is parallel to 
the axis of rotation; so that the right cone ASD, generated 
by the revolution of A S round S T, traces on the heavens 
a circle of declination, having the edge A of the ring for its 
upper culminating point: whereas the oblique cone A S B, 
tracing the visible course of the ring in the heavens, though 



23 The circumstances have been traced in minute detail by Dr. Lardner, who 
first, I believe, drew attention to the effect of situation on the surface of the 
planet in modifying the phenomena presented by the rings. 



440 OUTLINES OF ASTRONOMY 

coincident with the former at its upper culmination A, lies 
elsewhere wholly exterior to it, and has its inferior culmina- 
tion B nearer to the elevated pole by the angle BSD, the 
difference of the angles of the two cones. The apparent 
course of either edge of the ring, then, is a curve touching 
the circle of declination at which that edge culminates, but 
receding from it toward the elevated pole, so as to allow 
stars or the Sun to be visible at certain seasons under the 
ring at their rising — to be eclipsed wholly or partially by it 
at its under edge, and again to emerge before setting. This 
will not prevent, however, some considerable regions of Sat- 
urn from suffering very long total interception of the solar 
beams, affording, to our ideas, but an inhospitable asylum 
to animated beings, ill compensated by the feeble light of 
the satellites. But we shall do wrong to judge of the fitness 
or unfitness of their condition from what we see around us, 
when perhaps the very combinations which convey to our 
minds only images of horror, may be, in reality, theatres of 
the most striking and glorious displays of beneficent con- 
trivance. 

(523.) Of Uranus we see nothing but a small round uni- 
formly illuminated disk, without rings, belts, or discernible 
spots. Its apparent diameter is about 4", from which it 
never varies much, owing to the smallness of our orbit in 
comparison of its own. Its real diameter is about 35,000 
miles, and its bulk 82 times that of the earth. It is attended 
by four satellites, whose existence may be considered as 
conclusively established (and more have been suspected). 

(524.) The discovery of Neptune is so recent, and its 
situation in the ecliptic at present so little favorable for see- 
ing it with perfect distinctness, that nothing very positive 
can be stated as to its physical appearance. It was at first 



OUTLINES OF ASTRONOMY 441 

suspected to have a ring, but the suspicion has not been 
verified. It is attended by at least one satellite, the exist- 
ence of which has been demonstrated by the observations of 
Mr. Lassell, M. Otto Struve, and Mr. Bond. 

(525.) If the immense distance of Neptune precludes all 
hope of coming at much knowledge of its physical state, the 
minuteness of the Asteroids is no less a bar to any inquiry 
into theirs. One of them, Pallas, has been said to have 
somewhat of a nebulous or hazy appearance, indicative of 
an extensive and vaporous atmosphere, little repressed and 
condensed by the inadequate gravity of so small a mass. It 
is probable, however, that the appearance in question has 
originated in some imperfection in the telescope employed, 
or other temporary causes of illusion. In Vesta and Pallas 
only have sensible disks been hitherto observed, and those 
only with very high magnifying powers. Vesta was once 
seen by Schroter with the naked eye. No doubt the most 
remarkable of their peculiarities must lie in this condition 
of their state. A man placed on one of them would spring 
with ease 60 feet high, and sustain no greater shock in his 
descent than he does on the earth from leaping a yard. On 
such planets giants might exist; and those enormous ani- 
mals, which on earth require the buoyant power of water to 
counteract their weight, might there be denizens of the land. 
From some recent researches of M. Leverrier, it appears that 
we shall be warranted in attributing to the totality of the 
Asteroids a quantity of matter quite insignificant. 

(525 a.) There is a remarkable division of the planetary 
system into two families or classes of planets, the large, and 
the small. To the latter family belong those interior to the 
orbits of Jupiter, viz. Mercury, Venus, the Earth, and Mars, 
with the Asteroids. To the former, all exterior to the orbits 



442 OUTLINES OF ASTRONOMY 

of the first ciass — Jupiter, Saturn, Uranus, and Neptune. 
The Asteroids themselves, however, may be considered as 
forming a family apart, their magnitudes being as much in- 
ferior to those of the interior planets as these are to the ex- 
terior, or in a still lower ratio. Not less remarkable is the 
circumstance that while all the interior planets revolve on 
their axes (so far as is known) in about the same time (24 k ), 
the exterior (as is certain in the case of Jupiter and Saturn 
at least) have periods of rotation less than half that length. 
In point of density, too, as we shall see further on, an 
equally marked distinction of specific character is preserved, 
all the interior ones having about the same density as the 
Earth, while that of all the exterior is very much less, not 
exceeding a quarter of the Earth's, and agreeing (in the 
cases of Jupiter and Uranus) very closely with that of the 
Sun. 

(526.) We shall close this chapter with an illustration 
calculated to convey to the minds of our readers a general 
impression of the relative magnitudes and distances of the 
parts of our system. Choose any well levelled field or bowl- 
ing-green. On it place a globe, two feet in diameter; this 
will represent the Sun; Mercury will be represented by a 
grain of mustard seed, on the circumference of a circle 164 
feet in diameter for its orbit; Yenus a pea, on a circle of 
284 feet in diameter; the Earth also a pea, on a circle 
of 430 feet; Mars a rather large pin's head, on a circle of 
654 feet; the Asteroids, grains of sand, in orbits of from 
1000 to 1200 feet; Jupiter a moderate- sized orange, in a cir- 
cle nearly half a mile across; Saturn a small orange, on a 
circle of four-fifths of a mile; Uranus a full-sized cherry, or 
small plum, upon the circumference of a circle more than a 
mile and a half; and Neptune a good-sized plum, on a circle 



OUTLINES OF ASTRONOMY 443 

about two miles and a half in diameter. As to getting cor- 
rect notions on this subject by drawing circles on paper, or, 
still worse, from those very childish toys called orreries, it 
is out of the question. To imitate the motions of the plan- 
ets, in the above-mentioned orbits, Mercury must describe 
its own diameter in 41 seconds; Yenus, in4 m 14 8 ; the Earth, 
in 7 minutes; Mars, in 4 m 48 s ; Jupiter, 2 h 56 m ; Saturn, in 
3 h 13 m ; Uranus, in 2 h 16 m ; and Neptune, in 3 h 30 m . 24 



24 In the "Penny Encyclopaedia," vol. 22, p. 197, the diameters of the orbits 
of the planets here set down, are quoted as their distances from the centre, and 
the size of the sun is enlarged to four feet, while the sizes of the planets are 
unaltered. 



444 OUTLINES OF ASTRONOMY 



CHAPTER X 

OF THE SATELLITES 

Of the Moon, as a Satellite of the Earth — General Proximity of Satellites 
to their Primaries, and Consequent Subordination of their Motions — 
Masses of the Primaries Concluded from the Periods of their Satellites 
— Maintenance of Kepler's Laws in the Secondary Systems — Of Jupi- 
ter's Satellites — Their Eclipses, etc. — Telocity of Light Discovered 
by their Means — Satellites of Saturn — Of Uranus — Of Neptune 

(527.) In the annual circuit of the earth about the sun, 
it is constantly attended by its satellite, the moon, which 
revolves round it, or rather both round their common centre 
of gravity; while this centre, strictly speaking, and not 
either of the two bodies thus connected, moves^ in an ellip- 
tic orbit, undisturbed by their mutual action, just as the 
centre of gravity of a large and small stone tied together 
and flung into the air describes a parabola as if it were a 
real material substance under the earth's attraction, while 
the stones circulate round it or round each other, as we 
choose to conceive the matter. 

(528.) If we trace, therefore, the real curve actually de- 
scribed by either the moon's or the earth's centres, in virtue 
of this compound motion, it will appear to be, not an exact 
ellipse, but an undulated curve, like that represented in the 
figure to article 324, only that the number of undulations 
in a whole revolution is but 13, and their actual deviation 
from the general ellipse, which serves them as a central line, 
is comparatively very much smaller— so much so, indeed, 



OUTLINES OF ASTRONOMY 445 

that every part of the curve described by either the earth 
or moon is concave toward the sun. The excursions of the 
earth on either side the ellipse, indeed, are so very small 
as to be hardly appreciable. In fact, the centre of gravity 
of the earth and moon lies always within the surface 
of the earth, so that the monthly orbit described by the 
earth's centre about the common centre of gravity is com- 
prehended within a space less than the size of the earth 
itself. The effect is, nevertheless, sensible, in producing 
an apparent monthly displacement of the sun in longitude, 
of a parallactic kind, which is called the menstrual equation; 
whose greatest amount is, however, less than the sun's 
horizontal parallax, or than 8 # 6*. 

(529.) The moon, as we have seen, is about 60 radii of 
the earth distant from the centre of the latter. Its prox- 
imity, therefore, to its centre of attraction, thus estimated, 
is much greater than that of the planets to the sun ; of which 
Mercury, the nearest, is 84, and Uranus 2026 solar radii 
from its centre. It is owing to this proximity that the moon 
remains attached to the earth as a satellite. Were it much 
further, the feebleness of its gravity toward the earth would 
be inadequate to produce that alternate acceleration and 
retardation in its motion about the sun, which divests 
it of the character of an independent planet, and keeps 
its movements subordinate to those of the earth. The one 
would outrun, or be left behind the other, in their revolu- 
tions round the sun (by reason of Kepler's third law), 
according to the relative dimensions of their heliocentric 
orbits, after which the whole influence of the earth would 
be confined to producing some considerable periodical dis- 
turbance in the moon's motion, as it passed or was passed 
by it in each synodical revolution. 



446 OUTLINES OF ASTRONOMY 

(530.) At the distance at which the moon really is from 
us, its gravity toward the earth is actually less than toward 
the sun. That this is the case appears sufficiently from 
what we have already stated, that the moon's real path, 
even when between the earth and sun, is concave toward 
the latter. But it will appear still more clearly if, from 
the known periodic times 1 in which the earth completes 
its annual and the moon its monthly orbit, and from the 
dimensions of those orbits, we calculate the amount of de- 
flection in either, from their tangents, in equal very minute 
portions of time, as one second. These are the versed sines 
of the arcs described in that time in the two orbits, and 
these are the measures of the acting forces which pro- 
duce those deflections. If we execute the numerical cal- 
culation in the case before us, we shall find 2*233 : 1 
for the proportion in which the intensity of the force 
which retains the earth in its orbit round the sun actu- 
ally exceeds that by which the moon is retained in its 
orbit about the earth. 

(531.) Now the sun is about 400 times more remote from 
the earth than the moon is. And, as gravity increases as 
the squares of the distances decrease, it must follow that 
at equal distances, the intensity of solar would exceed that 
of terrestrial gravity in the above proportion, augmented 
in the further ratio of the square of 400 to 1 ; that is, in the 



OUTLINES OF ASTRONOMY 447 

proportion of 355,000 to 1 ; and therefore, if we grant that 
the intensity of the gravitating energy is commensurate with 
the mass or inertia of the attracting body, we are compelled 
to admit the mass of the earth to be no more than uftoo of 
that of the sun. 9 

(532.) The argument is, in fact, nothing more than a re- 
capitulation of what has been adduced in Chap. VIII (art. 
448). But it is here re-introduced, in order to show how the 
mass of a planet which is attended by one or more satellites 
can be as it were weighed against the sun, provided we have 
learned, from observation, the dimensions of the orbits de- 
scribed by the planet about the sun, and by the satellites 
about the planet, and also the periods in which these orbits 
are respectively described. It is by this method that the 
masses of Jupiter, Saturn, Uranus, and Neptune have been 
ascertained, and from which their densities are concluded. 
(See art. 561.) 

(533.) Jupiter, as already stated, is attended by four 
satellites; Saturn by eight; Uranus certainly by four; and 
Neptune by one, or possibly more. These, with their re- 
spective primaries (as the central planets are called) form 
in each case miniature systems entirely analogous, in the 
general laws by which their motions are governed, to the 
great system in which the sun acts the part of the primary, 
and the planets of its satellites. In each of these systems 
the laws of Kepler are obeyed, in the sense, that is to say, 
in which they are obeyed in the planetary system — approxi- 
mately, and without prejudice to the effects of mutual per- 



2 In the synoptic table at the end of this volume, the mass of the sun is 
taken somewhat higher, according to the most recent determination. It has 
not been thought worth while to alter all the figures of the text in conformity 
with that estimate. 



448 OUTLINES OF ASTRONOMY 

turbation, of extraneous interference, if any, and of that 
small but not imperceptible correction which arises from 
the elliptic form of the central body. Their orbits are 
circles or ellipses of very moderate excentricity, the pri- 
mary occupying one focus. About this they describe areas 
very nearly proportional to the times; and the squares of 
the periodical times of all the satellites belonging to each 
planet are in proportion to each other as the cubes of their 
distances. The tables at the end of the volume exhibit a 
synoptic view of the distances and periods in these several 
systems, so far as they are at present known; and to all of 
them it will be observed that the same remark respect- 
ing their proximity to their primaries holds good, as in 
the case of the moon, with a similar reason for such close 
connection. 

(534.) Of these systems, however, the only one which has 
been studied with attention to all its details, is that of Ju- 
piter; partly on account of the conspicuous brilliancy of its 
four attendants, which are large enough to offer visible and 
measurable disks in telescopes of great power; but more 
for the sake of their eclipses, which, as they happen very 
frequently, and are easily observed, afford signals of con- 
siderable use for the determination of terrestrial longi- 
tudes (art. 286). This .method, indeed, until thrown into 
the background by the greater facility and exactness now 
attainable by lunar observations (art. 287), was the best, 
or rather the only one which could be relied on for great 
distances and long intervals. 

(535.) The satellites of Jupiter revolve from west to east 
(following the analogy of the planets and moon), in planes 
very nearly, although not exactly, coincident with that of 
the equator of the planet, or parallel to its belts. This latter 



OUTLINES OF ASTRONOMY 449 

plane is inclined 3° 5' 30" to the orbit of the planet, and is 
therefore but little different from the plane of the ecliptic. 
Accordingly, we see their orbits projected very nearly into 
straight lines, in which they appear to oscillate to and fro, 
sometimes passing before Jupiter, and casting shadows on 
his disk (which are very visible in good telescopes, like 
small round ink spots, the circular form of which is very 
evident), and sometimes disappearing behind the body, 
or being eclipsed in its shadow at a distance from it. It 
is by these eclipses that we are furnished with accurate 
data for the construction of tables of the satellites' mo- 
tions, as well as with signals for determining differences 
of longitude. 

(536.) The eclipses of the satellites, in their general con- 
ception, are perfectly analogous to those of the moon, but 
in their detail they differ in several particulars. Owing to 
the much greater distance of Jupiter from the sun, and its 
greater magnitude, the cone of its shadow or umbra (art. 
420) is greatly more elongated, and of far greater dimen- 
sions, than that of the earth. The satellites are, moreover, 
much less in proportion to their primary, their orbits less 
inclined to its ecliptic, and (comparatively to the diame- 
ter of the planet) of smaller dimensions, than is the case 
with the moon. Owing to these causes, the three interior 
satellites of Jupiter pass through the shadow, and are 
totally eclipsed, every revolution; and the fourth, though, 
from the greater inclination of its orbit, it sometimes 
escapes eclipse, and may occasionally graze as it were the 
border of the shadow, and suffer partial eclipse, yet 
does so comparatively seldom, and, ordinarily speaking, 
its eclipses happen, like those of the rest, each revo- 
lution. 



450 OUTLINES OF ASTRONOMY 

(537.) These eclipses, moreover, are not seen, as is the 
case with those of the moon, from the centre of their mo- 
tion, but from a remote station, and one whose situation 
with respect to the line of shadow is variable. This, of 
course, makes no difference in the times of the eclipses, but 
a very great one in their visibility, and in their apparent 
situations with respect to the planet at the moments of their 
entering and quitting the shadow. 

(538.) Suppose S to be the sun, E the earth in its orbit 
E F Gr K, J Jupiter, and a b the orbit of one of its satellites. 
The cone of the shadow, then, will have its vertex at X, a 
point far beyond the orbits of all the satellites; and the 
penumbra, owing to the great distance of the sun, and the 
consequent smallness of the angle (about 6' only) its disk 
subtends at Jupiter, will hardly extend, within the limits of 
the satellites' orbits, to any perceptible distance beyond the 



~.X 




shadow — for which reason it is not represented in the figure. 
A satellite revolving from west to east (in the direction of 
the arrows) will be eclipsed when it enters the shadow at a, 
but not suddenly, because, like the moon, it has a consider- 
able diameter seen from the planet; so that the time elaps- 
ing from the first perceptible loss of light to its total extinc- 
tion will be that which it occupies in describing about 
Jupiter an angle equal to its apparent diameter as seen 
from the centre of the planet, or rather somewhat more, by 



OUTLINES OF ASTRONOMY 451 

reason of the penumbra ; and the same remark applies to its 

emergence at b. Now, owing to the difference of telescopes 
and of eyes, it is not possible to assign the precise moment 
of incipient obscuration, or of total extinction at a, nor that 
of the first glimpse of light falling on the satellite at b y or 
the complete recovery of its light. The observation of an 
eclipse, then, in which only the immersion, or only the 
emersion, is seen, is incomplete, and inadequate to afford 
any precise information, theoretical or practical. But, if 
both the immersion and emersion can be observed with the 
same telescope and by the same person, the interval of the 
times will give the duration, and their mean the exact 
middle of the eclipse, when the satellite is in the line 
S J X, i.e. the true moment of its opposition to the sun. 
Such observations, and such only, are of use for de- 
termining the periods and other particulars of the mo- 
tions of the satellites, and for affording data of any 
material use for the calculation of terrestrial longitudes. 
The intervals of the eclipses, it will be observed, give 
the synodic periods of the satellites' revolutions; from 
which their sidereal periods must be concluded by the 
method in art. 418. 

(539.) It is evident, from a mere inspection of our figure, 
that the eclipses take place to the west of the planet, when 
the earth is situated to the west of the line S J, i.e. before 
the opposition of Jupiter; and to the east, when in the other 
half of its orbit, or after the opposition. When the earth 
approaches the opposition, the visual line becomes more and 
more nearly coincident with the direction of the shadow, 
and the apparent place where the eclipses happen will be 
continually nearer and nearer to the body of the planet. 
When the earth comes to F, a point determined by drawing 



452 OUTLINES OF ASTRONOMY 

b F to touch the body of the planet, the emersions will cease 
to be visible, and will thenceforth, up to the time of the 
opposition, happen behind the disk of the planet. Simi- 
larly, from the opposition till the time when the earth 
arrives at I, a point determined by drawing a I tangent 
to the eastern limb of Jupiter, the immersions will be con- 
cealed from our view. When the earth arrives at Gr (or H) 
the immersion (or emersion) will happen at the very edge of 
the visible disk, and when between G and H (a very small 
space), the satellites will pass uneclipsed behind the limb of 
the planet. 

(540.) Both the satellites and their shadows are fre- 
quently observed to transit or pass across the disk of the 
planet. When a satellite comes to ra, its shadow will be 
thrown on Jupiter, and will appear to move across it as a 
black spot till the satellite comes to n. But the satellite 
itself will not appear to enter on the disk till it comes up to 
the line drawn from E to the eastern edge of the disk, and 
will not leave it till it attains a similar line drawn to the 
western edge. It appears then that the shadow will precede 
the satellite in its progress over the disk before the opposi- 
tion of Jupiter, and vice versd. In these transits of the 
satellites, which, with very powerful telescopes, may be 
observed with great precision, it frequently happens that 
the satellite itself is discernible on the disk as a bright spot 
if projected on a dark belt; but occasionally also as a dark 
spot of smaller dimensions than the shadow. This curious 
fact (observed by Schroter and Harding) has led to a con- 
clusion that certain of the satellites have occasionally on 
their own bodies, or in their atmospheres, obscure spots of 
great extent. We say of great extent; for the satellites 
of Jupiter, small as they appear to us, are really bodies 



OUTLINES OF ASTRONOMY 



453 



of considerable size, as the following comparative table 

•will show: — 3 





Mean apparent 


Mean apparent 








diameter as 


diameter as seen 


Diameter in 






seen from the 


from Jupiter's 


miles. 


Mass. 




earth. 


centre. 






Jupiter 


39". 91 




91128 


1-0000000 


1st satelite 


1-105 


33' 11" 


2508 


0-0000173 


2d 


0-911 


IT 35 


2068 


0-0000232 


3d 


1-488 


18 


3377 


0-0000885 


4th 


1-2*3 


8 46 


2890 


0-0000427 



From which it follows, that the first satellite appears, when 
on Jupiter's horizon, as large as our moon to us; the second 
and third nearly equal to each other, and of somewhat more 
than half the apparent diameter of the first, and the fourth 
about one quarter of that diameter. So seen, they will fre- 
quently, of course, eclipse one another, and cause eclipses 
of the sun (the latter visible, however, only over a very 
small portion of the planet), and their motions and aspects 
with respect to each other must offer a perpetual variety and 
singular and pleasing interest to the inhabitants of their 
primary. 

(541.) Besides the eclipses and the transits of the satel- 
lites across the disk, they may also disappear to us when not 
eclipsed, by passing behind the body of the planet. Thus, 
when the earth is at E, the immersion of the satellite will be 
seen at a, and its emersion at 5, both to the west of the 
planet, after which the satellite, still continuing its course 
in the direction b, will pass behind the body, and again 
emerge on the opposite side, after an interval of occultation 
greater or less according to the distance of the satellite. 
This interval (on account of the great distance of the earth 



3 Struve, Mem. Art. Soc. iii. 301. Main. Do. xxv. p. 51. 

4 Laplace, Mec. Cel. liv. viii. § 27. 



454 OUTLINES OF ASTRONOMY 

compared with the radii of the orbits of the satellites) varies 
but little in the case of each satellite, being nearly equal to 
the time which the satellite requires to describe an arc of its 
orbit, equal to the angular diameter of Jupiter as seen from 
its centre, which time, for the several satellites, is as fol- 
lows: viz. for the first, 2 h 20 m ; for the second, 2 h 56 m ; for the 
third, 3 h 43 m ; and for the fourth, 4 h 56 m ; the corresponding 
diameters of the planet as seen from these respective satel- 
lites being, 19° 49'; 12° 25'; 7° 47'; and 4° 25'. 6 Before the 
opposition of Jupiter, these occultations of the satellites 
happen after the eclipses: after the opposition (when, for in- 
stance, the earth is in the situation K), the occultations take 
place before the eclipses. It is to be observed, that, owing 
to the proximity of the orbits of the first and second satel- 
lites to the planet, both the immersion and emersion of either 
of them can never be observed in any single eclipse, the im- 
mersion being concealed by the body, if the planet be past 
its opposition, the emersion if not yet arrived at it. So also 
of the occultation. The commencement of the occultation, 
or the passage of the satellite behind the disk, takes place 
while obscured by the shadow, before opposition, and its 
re-emergence after. All these particulars will be easily ap- 
parent on mere inspection of the figure (art. 536). It is only 
during the short time that the earth is in the arc G H, i.e. 
between the sun and Jupiter, that the cone of the shadow 
converging (while that of the visual rays diverges) behind 
the planet, permits their occultations to be completely ob- 
served both at ingress and egress, unobscured, the eclipses 
being then invisible. 



5 These data are taken approximately from Mr. Woolhouse's paper in the 
supplement to the Nautical Almanack for 1835. 



OUTLINES OF ASTRONOMY 455 

(542.) An extremely singular relation subsists between 
the mean angular velocities or mean motions (as they are 
termed) of the three first satellites of Jupiter. If the mean 
angular velocity of the first satellite be added to twice that 
of the third, the sum will equal three times that of the sec- 
ond. From this relation it follows, that if from the mean 
longitude of the first, added to twice that of the third, be 
subducted three times that of the second, the remainder will 
always be the same, or constant, and observation informs us 
that this constant is 180°, or two right angles; so that the 
situations of any two of them being given, that of the third 
may be found. It has been attempted to account for this 
remarkable fact, on the theory of gravity by their mutual 
action; and Laplace has demonstrated, that if this relation 
were at any one epoch approximately true, the mutual at- 
tractions of the satellites would, in process of time, render 
it exactly so. One curious consequence is, that these three 
satellites cannot be all eclipsed at once; for, in consequence 
of the last-mentioned relation, when the second and third lie 
in the same direction from the centre, the first must lie on 
the opposite: and therefore, when at such a conjunction the 
first is eclipsed, the other two must lie between the sun and 
planet, throwing their shadows on the disk, and vice versd. 

(543.) Although, however, for the above-mentioned rea- 
son, the satellites cannot be all eclipsed at once, yet it may 
happen, and occasionally does so, that all are either eclipsed, 
occulted, or projected on the body, in which case they are, 
generally speaking, equally invisible, since it requires an 
excellent telescope to discern a satellite on the body, except 
in peculiar circumstances. Instances of the actual observa- 
tion of Jupiter thus denuded of its usual attendance and 
offering the appearance of a solitary disk, though rare, have 



456 OUTLINES OF ASTRONOMY 

been more than once recorded. The first occasion in which 
this was noticed was by Molyneux, on November 2 (old 
style), 1681/ A similar observation is recorded by Sir W. 
Herschel as made by him on May 23, 1802. The phenome- 
non has also been observed by Mr. Wallis, on April 15, 1826 
(in which case the deprivation continued two whole hours); 
and lastly by Mr. H. Grriesbach, on September 27, 1843. 

(544.) The discovery of Jupiter's satellites, one of the 
first fruits of the invention of the telescope, and of Galileo's 
early and happy idea of directing its new-found powers to 
the examination of the heavens, forms one of the most 
memorable epochs in the history of astronomy. The first 
astronomical solution of the great problem of ' ' the longitude 1 ' 
— practically the most important for the interests of man- 
kind which has ever been brought under the dominion of 
strict scientific principles, dates immediately from their dis- 
covery. The final and conclusive establishment of the 
Copernican system of astronomy may also be considered 
as referable to the discovery and study of this exquisite 
miniature system, in which the laws of the planetary mo- 
tions, as ascertained by Kepler, and especially that which 
connects their periods and distances, were speedily traced, 
and found to be satisfactorily maintained. And (as if to 
accumulate historical interest on this point), it is to the ob- 
servation of their eclipses that we owe the grand discovery 
of the successive propagation of light, and the determination 
of the enormous velocity of that wonderful element. This 
we must explain now at large. 

(545.) The earth's orbit being concentric with that of 
Jupiter and interior to it (see fig. art. 536), their mutual 

6 Molyneux, Optics, p. 271. 



OUTLINES OF ASTRONOMY 457 

distance is continually varying, the variation extending 
from the sum to the difference of the radii of the two orbits ; 
and the difference of the greater and least distances being 
equal to a diameter of the earth's orbit. Now, it was ob- 
served by Eoemer (a Danish astronomer, in 1675), on com- 
paring together observations of eclipses of the satellites 
during many successive years, that the eclipses at and 
about the opposition of Jupiter (or its nearest point to the 
earth) took place too soon — sooner, that is, than, by calcula- 
tion from an average, he expected them; whereas those 
which happened when the earth was in the part of its orbit 
most remote from Jupiter were always too late. Connecting 
the observed error in their computed times with the varia- 
tion of distance, he concluded, that, to make the calculation 
on an average period correspond with fact, an allowance in 
respect of time behooved to be made proportional to the 
excess or defect of Jupiter's distance from the earth above 
or below its average amount, and such that a difference of 
distance of one diameter of the earth's orbit should corre- 
spond to 16 m 26 s -6 of time allowed. Speculating on the 
probable physical cause, he was naturally led to think of 
a gradual instead of an instantaneous propagation of light. 
This explained every particular of the observed phenom- 
enon, but the velocity required (192,000 miles per second) 
was so great as to startle many, and, at all events, to require 
confirmation. This has been afforded since, and of the 
most unequivocal kind, by Bradley's discovery of the aber- 
ration of light (art. 329). The velocity of light deduced 
from this last phenomenon differs by less than one- eightieth 
of its amount from that calculated from the eclipses, and 
even this difference will no doubt be destroyed by nicer 

and more rigorously reduced observations. The velocity 
Astronomy— Vol. XIX. — 20 



458 OUTLINES OF ASTRONOMY 

has also been determined by M. Fizeau (by direct experi- 
ments with, a reflecting apparatus on a most ingenious prin- 
ciple, suggested by Mr. Wheatstone for measuring the 
velocity of the electric current) at 70,000 geographical 
leagues, 25 to the degree =194, 600 statute miles per 
second. 

(546.) The orbits of Jupiter's satellites are but little 
excentric; those of the two interior, indeed, have no per- 
ceptible excentricity. Their mutual action produces in 
them perturbations analogous to those of the planets about 
the sun, and which have been diligently investigated by 
Laplace and others. By assiduous observation it has been 
ascertained that they are subject to marked fluctuations in 
respect of brightness, and that these fluctuations happen 
periodically, according to their position with respect to the 
sun. From this it has been concluded, apparently with 
reason, that they turn on their axes, like our moon, in 
periods equal to their respective sidereal revolutions about 
their primary. 

(547.) The satellites of Saturn have been much less 
studied than those of Jupiter, being far more difficult to 
observe. The most distant has its orbit materially inclined 
(no less than 12° 14') 7 to the plane of the ring, with which 
the orbits of all the rest nearly coincide. Nor is this the 
only circumstance which separates it by a marked difference 
of character from the system of the seven inferior ones,, and 
renders it in some sort an anomalous member of the Satur- 
nian system. Its distance from the planet's centre is no 
less than 64 times the radius of the globe of Saturn, a dis- 
tance from the primary to which our own moon (at 60 radii) 

7 Lalande, Astron., Art. 3075. 



OUTLINES OF ASTRONOMY 459 

offers the only parallel. Its variation of light also in differ- 
ent parts of its orbit is very much greater than in the case 
of any other secondary planet. Dominic Cassini indeed (its 
first discoverer, A.D. 1671) found it to disappear for nearly 
half its revolution when to the east of Saturn, and though 
the more powerful telescopes now in use enable us to follow 
it round the whole of its circuit, its diminution of light is 
so great in the eastern half of its orbit as to render it some- 
what difficult to perceive. From this circumstance (viz. 
from the defalcation of light occurring constantly on the 
same side of Saturn as seen from the earth, the visual ray 
from which is never very oblique to the direction in which 
the sun's light falls on it) it is presumed, with much cer- 
tainty, that this satellite revolves on its axis in the exact 
time of rotation about the primary ; as we know to be the 
case with the moon, and as there is considerable ground for 
believing to be so with all secondaries. 

(548.) The next satellite in order, proceeding inward (as 
it used to be considered until the recent discovery of an in- 
termediate one), was the first to be detected. 8 It is by far 
the largest and most conspicuous of all, and is probably not 
much inferior to Mercury in size. It is the only one of the 
number whose theory and perturbations have been at all 
inquired into" further than to verify Kepler's law of the 
periodic times, which holds good, mutatis mutandis, and 
under the requisite reservations, in this, as in the system 
of Jupiter. The next three satellites, still proceeding in- 
ward, 10 are very minute, and require pretty powerful tel- 
escopes to see them ; while the two interior satellites, which 



8 By Huyghens, March 25, 1655. 

9 By Bessel, Astr. Nachr. Nos. 193, 214. 

10 Discovered by Dominic Cassini in 16?2 and 1684. 



460 OUTLINES OF ASTRONOMY 

just skirt the edge of the ring, 11 can only be seen with 
telescopes of extraordinary power and perfection, and under 
the most favorable atmospheric circumstances. At the 
epoch of their discovery they were seen to thread, like 
beads, the almost infinitely thin fibre of light to which 
the ring, then seen edgewise, was reduced, and for a short 
time to advance off it at either end, speedily to return, and 
hastening to their habitual concealment behind or on the 
body. An eighth very faint satellite has been recently de- 
tected (between the two outermost of the old satellites) simul- 
taneously (within the same hour) by Mr. Dawes, Mr. Lassell, 
and Professor Bond, 13 the two former observing together in 
Mr. LasseU's observatory at Starfield, the latter in that of 
Cambridge, U. S. 

(549.) Owing to the obliquity of the ring and of the orbits 
of the satellites to Saturn's ecliptic, there are no eclipses, 



11 Discovered by Sir William Herschel in 1*789. 

12 On the night of the 19th of September, 1848. Considerable confusion used 
already to prevail, before the discovery of this satellite, in the nomenclature of 
the saturnian system, owing to the order of discovery not coinciding with that 
of distances. Astronomers were not agreed whether to call the two interior 
satellites the 6th and 7th (reckoning inward) and the older ones the 1st, 2d, 
3d, 4th and 5th, reckoning outward; or to commence with the innermost and 
reckon outward, from 1 to 7. This confusion, which the introduction of an 
eighth would have rendered intolerable, has been obviated by a mythological 
nomenclature, suggested in a former edition of this work, and which has been 
generally accepted, in consonance with that at length completely established for 
the primary planets. Taking the names of the Titanian divinities, the following 
verses (pardoning false quantities) afford an easy artificial memory. 

Iapetus cunctos supra rotat, huncce sequuntur 
Hyperion, Titan, Rhea, Dione, Tethys, 
Enceladus, Mimas — 

It is worth remarking that Simon Marius, who disputed the priority of ths 
discovery of Jupiter's satellites with Galileo, proposed for them mythological 
names, viz. Io, Europa, Ganymede and Callisto. The revival of these names 
would savor of a preference of Marius's claim, which, even if an absolute 
priority were conceded (which it is not), would still leave Galileo's general 
claim to the use of the telescope as a means of astronomical discovery intact. 
But in the case of Jupiter's satellites there exists no confusion to rectify. They 
are constantly referred to by their numerical designations in every almanac. 



OUTLINES OF ASTRONOMY 461 

occupations, or transits of these bodies or their shadows 
across the disk of their primary (the interior ones excepted), 
until near the time when the ring is seen edgewise, and 
when they do take place their observation is attended with 
too much difficulty to be of any practical use, like the 
eclipses of Jupiter's satellites for the determination of 
longitudes, for which reason they have been hitherto little 
attended to by astronomers. 

(550.) A remarkable relation subsists between the peri- 
odic times of the two interior satellites of Saturn and those 
of the two next in order of distance; viz. that the period of 
the third (Tethys) is double that of the first (Mimas), and 
that of the fourth (Dione) double that of the second (Encel- 
adus). The coincidence is exact in either case to about one 
800th part of the larger period. 

(551.) The satellites of Uranus require very powerful 
and perfect telescopes for their observation. Four are cer- 
tainly known to exist, to which (proceeding from without, 
inward in succession) the names Oberon, Titania, Umbriel, 
and Ariel, of the fairies, sylphs, and gnomes of Shakespeare 
and Pope, have been assigned respectively. Of these Oberon 
and Titania are tolerably conspicuous in a reflecting telescope 
of 18 or 20 inches in aperture. They were discovered by Sir 
W. Herschel in 1787, and have since been reobserved by the 
author of this work, and subsequently by Messrs. Lassell, 
Otto Struve, and Lamont. Umbriel (a much fainter object) 
was also very probably seen by Sir W. Herschel, and de- 
scribed by him as "an interior satellite," but his observa- 
tions of it were not sufficiently numerous and precise to 
place its existence, at that time, beyond question. It was 
rediscovered, however, by M. Otto Struve, 18 and observed 

18 October 8, 1847. 



462 OUTLINES OF ASTRONOMY 

subsequently, on numerous occasions, by Mr. Lassell, to 
whom we also owe the first discovery of Ariel, 14 as well as 
a fine series of observations and micrometrical measures 
of all four, obtained at his observatory at Liverpool and 
during his residence in Malta in 1852-63, which forms a 
remarkable epoch in the history of astronomical observa- 
tion. Three other satellites, one intermediate between 
Oberon and Titania, the others exterior to both, were sus- 
pected by Sir W. Herschel, but their existence has not been 
confirmed. The periods and distances of the four known 
satellites will be found in the synoptic table at the end of 
the volume. 

(552.) The orbits of these satellites offer remarkable, ami, 
indeed, quite unexpected and unexampled peculiarities. 
Contrary to the unbroken analogy of the whole planetary 
system — whether of primaries or secondaries — the planes of 
their orbits are nearly perpendicular to the ecliptic, being 
inclined no less than 78° 58' to that plane, and in these 
orbits their motions are retrograde) that is to say, their 
positions, when projected on the ecliptic, instead of ad- 
vancing from west to east round the centre of their primary, 
as is the case with every other planet and satellite, move in 
the opposite direction. Their orbits are nearly or quite 
circular, and they do not appear to have any sensible, or, 
at least, any rapid motion of nodes, or to have undergone 
any material change of inclination, in the course, at least, 
of half a revolution of their primary round the sun. When 
the earth is in the plane of their orbits, or nearly so, their 
apparent paths are straight lines or very elongated ellipses, 
in which case they become invisible, their feeble light being 
effaced by the superior light of the planet, long before they 

14 September 14, 1847. 



OUTLINES OF ASTRONOMY 463 

come up to its disk, so that the observations of any eclipses 
or occultations they may undergo is quite out of the question 
with our present telescopes. 

(553.) If the observation of the satellites of Uranus be 
difficult, those of Neptune, owing to the immense distance 
of that planet, may be readily imagined to offer still greater 
difficulties. Of the existence of two, discovered by Mr. 
Lassell, 16 there can remain no doubt, having also been ob- 
served by other astronomers, both in Europe and America. 
According to M. Otto Struve 16 the orbit of the first is in- 
clined to the ecliptic at the considerable angle of 35°; but 
whether, as in the case of the satellites of Uranus, the direc- 
tion of its motion be retrograde it is not possible to say 
until it shall have been longer observed. 



15 On July 7, 1847 (suspected in 1846), and August 14, 1850. 

16 Astron. Nackr. No. 629, from his own observation, September 11 to 
December 20, 1847. 



KND Or PART I. OF "OUTLINES OP ASTRONOMY 



